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3.5146601881617107`*^9, { 3.525866119991829*^9, 3.5258661279332123`*^9}}], Cell["Seth J. Chandler", "Subtitle", CellChangeTimes->{{3.485609136120798*^9, 3.4856091511532907`*^9}, { 3.4856091945334663`*^9, 3.485609199379443*^9}, {3.4951031489375*^9, 3.49510314984375*^9}, {3.495106455296875*^9, 3.495106455453125*^9}, { 3.5143083846926413`*^9, 3.514308395249558*^9}, {3.5258661320835257`*^9, 3.5258661348959312`*^9}}], Cell["\<\ University of Houston Law Center, Program on Law and Computation\ \>", "Subsubtitle", CellChangeTimes->{ 3.483202458953512*^9, {3.495105345328125*^9, 3.495105347890625*^9}, { 3.49510644571875*^9, 3.495106448390625*^9}, {3.5143083980990458`*^9, 3.514308409442589*^9}, {3.525866137799053*^9, 3.525866145156485*^9}}], Cell["schandler@uh.edu", "Text", CellChangeTimes->{{3.527935825350286*^9, 3.52793583736786*^9}}], Cell[TextData[ButtonBox["http : // www.law.uh.edu/polac", BaseStyle->"Hyperlink", ButtonData->{ URL["http://www.law.uh.edu/polac"], None}, ButtonNote->"http://www.law.uh.edu/polac"]], "Text", CellChangeTimes->{{3.5279358461090097`*^9, 3.527935887187181*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Abstract", "Section", CellChangeTimes->{ 3.483202458955147*^9, {3.514308340990994*^9, 3.514308352103572*^9}, { 3.525866160130187*^9, 3.525866162086742*^9}}], Cell["\<\ Insurers cluster. They generally group insurance applicants with similar \ perceived risk levels together and offer each group different contracts. This \ practice, particularly where fine-grained, reduces adverse selection that \ otherwise prevents desirable trade in risk. The practice also tends, \ however, to replicate inequalities in original endowments of risk that may be \ no fault of the insured. Coarse classification by contrast, may reduce \ inequalities resulting from factors that are no fault of the insured but may \ also result in incomplete risk transfer due to adverse selection. Hitherto, most scholarship involving regulation of these insurance \ underwriting practices has considered clustering based on only one-dimension \ -- perceived risk -- and has correlatively involved offers that vary in only \ one feature -- price. This simplification is due in substantial part to the \ difficulties in modeling more complex clustering and contracting. This talk looks at how the symbolic and numeric capabilities of Mathematica \ can collaborate to permit more realistic models of insurance underwriting and \ thus more realistic appraisals of justice in the regulation of insurance \ underwriting. It considers \[OpenCurlyDoubleQuote]two dimensional \ underwriting\[CloseCurlyDoubleQuote] in which insurers cluster proposed \ insureds based not only on the perceived level of risk the insured might pose \ without undertaking risk avoidance but also on the effective price the \ insured faces to reduce risk. It correlatively considers contracts that vary \ in two ways: the price charged and the level of care demanded. Particular \ emphasis is placed on the statistical capabilities advanced in Version 8. The \ ambition of the project is to generate models that produce results in \ \[OpenCurlyDoubleQuote]real time.\[CloseCurlyDoubleQuote]\ \>", "Text", CellChangeTimes->{{3.495209008234375*^9, 3.49520915653125*^9}, 3.495209919765625*^9, 3.4952106014375*^9, {3.4952106824375*^9, 3.495210832234375*^9}, 3.514307848543872*^9, {3.514308058576482*^9, 3.514308065607885*^9}, {3.51430841745117*^9, 3.514308419642997*^9}, { 3.5149152616687326`*^9, 3.514915280523456*^9}, {3.514915328702818*^9, 3.5149153375415287`*^9}, 3.514915444638068*^9, {3.525866295394919*^9, 3.525866304615947*^9}, 3.525866344812046*^9, 3.525866385360113*^9, 3.5267242965559053`*^9, {3.526724343354719*^9, 3.526724346436576*^9}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Why You Should Care", "Section", CellChangeTimes->{ 3.483202458955147*^9, {3.51430857274755*^9, 3.514308578875259*^9}, { 3.525866168218581*^9, 3.525866171222579*^9}}], Cell[CellGroupData[{ Cell["Reason 1: Justice", "Subsection", CellChangeTimes->{{3.525951235274876*^9, 3.5259512456353703`*^9}, 3.525954845664069*^9}], Cell[CellGroupData[{ Cell["Theory", "Subsubsection", CellChangeTimes->{{3.526124263235935*^9, 3.526124272111952*^9}}], Cell["\<\ A lot of contemporary debate in the United States and elsewhere is about \ distribution of wealth and income. Access to insurance markets affects the \ distribution of income and, in some instances, affects life trajectories.\ \>", "Text", CellChangeTimes->{{3.525949144435541*^9, 3.525949192156752*^9}, { 3.527940089476342*^9, 3.527940090849308*^9}}], Cell[BoxData[ RowBox[{ GraphicsBox[ TagBox[RasterBox[CompressedData[" 1:eJzMvfnfX9O5/9/P4/snfB7ncbSUiChiSshAZJ4nQ1CSJoYQQSRq1hAxJogg pgiSkIiaa0iPcjh0QNWh2upwqj3aHvRoqSDmof08v+v52NdjZe/33vf7vt3a rh/e9773e7/3Xntdr/W6rnWta11r6yO+vv8R/98XvvCF//t/vvCFp/j7/x/v XpTdUulblD41ZddOll1qys41pfTVTpWyY3ul+kNL3XtV38561t0nntJQ1Xaq 3fyrvPiU6q/qWrJrpZ062DK2ku1GlXr16rX11ltvs802HPTs2fOfHFddhlZd y9TVp65udffpLK66peyccFU6072l+ekho4CWUKFW2267LXASV3z+o3DVvmSr L/tZcNXQaJ19RAlXXYNWF+Tb8uedvf9nKbmkugtXncVbHXLaub6hqbuMqzav 7wKomstnlPvfDTPtlKoce/fuDZZ69OghtFCIdbiqK/9AXFnalH6dHNuRb2d/ 1VDbTsmogbebK9zw9Ob7d61UH7399tuDpa222gpoccDnPxuuqj+ptlU70GoH Py3bv+5BdXdrqOdnkW+0Q7UmnzdsOixVcYirLbfcUlwBsH9CXHUIrc8DV3X3 b76mJNku4KqddsirVHfbzrZ/F+pTfc2d0jiIgx122AENCJy2TuUfyFcdvld+ 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What I want to \ do here is combine and formalize some ideas of the philosopher John Rawls and \ the Nobel prize winning economist John Harsanyi and imagine ourselves behind \ a veil of ignorance where we do not know what sort of person we are going to \ be when we emerge from behind the veil. We might simply know a distribution \ of possible persons. We could evaluate our behind-the-veil position by a \ single number and thus compare possible distributions if we took a weighted \ average of the wealth or happiness associated with being each person. Our \ weighting function would depend on our risk aversion but it would likely be a \ function that was non-increasing as we went from being in the worst possible \ position to the best possible position. In ", StyleBox["Mathematica", FontSlant->"Italic"], " terms we could calculate the expected quantile of the distribution with \ quantiles drawn from a behind-the-veil weighting function that met the \ following three criteria:" }], "Text", CellChangeTimes->{{3.525949495822103*^9, 3.5259496481560497`*^9}, { 3.525949680218882*^9, 3.525949685562508*^9}, {3.525949771108881*^9, 3.525949944046647*^9}, {3.525949977988173*^9, 3.525950119961342*^9}, { 3.5259501543999977`*^9, 3.525950363008226*^9}, {3.525950810569997*^9, 3.525950814046276*^9}, 3.527939963549718*^9}], Cell[CellGroupData[{ Cell["CDF[distribution, 0] == 0", "ItemNumbered", CellChangeTimes->{{3.525950368757436*^9, 3.525950391611124*^9}}], Cell["CDF[distribution, 1] == 1", "ItemNumbered", CellChangeTimes->{{3.525950381625074*^9, 3.525950408403439*^9}}], Cell[TextData[Cell[BoxData[ FormBox[ RowBox[{ SubscriptBox["\[ForAll]", RowBox[{"q", ",", RowBox[{"0", "<", "q", "\[LessEqual]", "1"}]}]], RowBox[{ RowBox[{ SubscriptBox["\[PartialD]", "q"], RowBox[{"PDF", "[", RowBox[{"distribution", ",", "q"}], "]"}]}], "\[LessEqual]", "0"}]}], TraditionalForm]]]], "ItemNumbered", CellChangeTimes->{{3.5259505439491243`*^9, 3.5259506086291857`*^9}}] }, Open ]], Cell["\<\ This compression of a wealth distribution to a single measure is generally \ known as a spectral measure.\ \>", "Text", CellChangeTimes->{{3.525950663336204*^9, 3.525950713685596*^9}, { 3.525950823091299*^9, 3.5259509260520353`*^9}, {3.525952326562504*^9, 3.5259523337395773`*^9}, {3.525954363587785*^9, 3.525954367852387*^9}, { 3.527775132186092*^9, 3.527775149037673*^9}}], Cell["\<\ I claim that the distribution of wealth once we have emerged from the veil is \ a function of the interaction between the system of insurance regulation \ \[ScriptCapitalR] and a number of other factors such as the distribution of \ risks that individuals pose if they make no effort to reduce them and the \ distribution of costs that individuals face in an effort to reduce risk. 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Cell[CellGroupData[{ Cell["Reason 2: Mathematica", "Subsection", CellChangeTimes->{ 3.483202458956718*^9, {3.514308604990972*^9, 3.514308608117634*^9}, { 3.525875385723113*^9, 3.525875386827224*^9}, {3.525949137819025*^9, 3.525949139675022*^9}}], Cell[TextData[{ "I have stated the problem at a very abstract level. The ambition is to use ", StyleBox["Mathematica", FontSlant->"Italic"], " to make it concrete and computable. My second ambition is to make this \ complex system computable in real time. This is a large multi-factorial \ system. Exploring the entire space of possibilities is difficult. So the \ faster I can traverse different possibilities such as different degrees of \ after-veil risk aversion or different classification algorithms adopted by \ insurers, the more I can get a feel for the factors that make a difference. \ I\[CloseCurlyQuote]ve been playing with this problem for a long time and I \ finally think that with ", StyleBox["Mathematica", FontSlant->"Italic"], " 8, I have made some substantial progress. My hope is that even if you work \ in a field far different from me, there is enough creativity in the use of \ Mathematica here to make this talk of interest." }], "Text", CellChangeTimes->{{3.525950953661289*^9, 3.5259511635181932`*^9}, 3.526124539205965*^9, {3.527939979059848*^9, 3.527939997559415*^9}}] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["The formal idea", "Section", CellChangeTimes->{ 3.483202458955147*^9, {3.514308863196991*^9, 3.5143088633311243`*^9}, { 3.525866412706142*^9, 3.525866423537642*^9}}], Cell[CellGroupData[{ Cell["\<\ Insureds can suffer a loss of \[ScriptL] from an insured event. \ \>", "ItemNumbered", CellChangeTimes->{{3.525866434699778*^9, 3.525866462834154*^9}, { 3.525866500748682*^9, 3.525866740091436*^9}, {3.525866823161943*^9, 3.525866823555791*^9}, {3.525867092633954*^9, 3.525867093072784*^9}, { 3.525867381007032*^9, 3.5258673813205433`*^9}, {3.525871470750758*^9, 3.525871485139741*^9}}], Cell["Insureds have three immutable characteristics", "ItemNumbered", CellChangeTimes->{{3.525866434699778*^9, 3.525866462834154*^9}, { 3.525866500748682*^9, 3.525866740091436*^9}, {3.525866823161943*^9, 3.525866823555791*^9}, {3.525867092633954*^9, 3.525867093072784*^9}, { 3.525867381007032*^9, 3.5258673813205433`*^9}, {3.525871470750758*^9, 3.525871485139741*^9}, {3.525875807791286*^9, 3.52587584804469*^9}, { 3.525953920550604*^9, 3.525953953133563*^9}, 3.5259540247369843`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Grid", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "Symbol", ",", "\"\\"", ",", "\"\\"", ",", "\"\\""}], "}"}], ",", RowBox[{"{", RowBox[{ "\"\\"", ",", "\"\\"", ",", "\"\\"", ",", "\"\<(0,1)\>\""}], "}"}], ",", RowBox[{"{", RowBox[{ "\"\\"", ",", "\"\\"", ",", "\"\\"", ",", "\"\<(0,\[Infinity])\>\""}], "}"}], ",", RowBox[{"{", RowBox[{ "\"\<\[Phi]\>\"", ",", "\"\\"", ",", "\"\\"", ",", "\"\<[0,1]\>\""}], "}"}]}], "}"}], ",", RowBox[{"Dividers", "\[Rule]", "All"}], ",", RowBox[{"Background", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"ColorData", "[", "42", "]"}], "[", "1", "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{"ColorData", "[", "42", "]"}], "[", "2", "]"}], "}"}]}], "}"}]}], ",", RowBox[{"BaseStyle", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"FontFamily", "\[Rule]", "\"\\""}], ",", RowBox[{"FontSize", "\[Rule]", "14"}]}], "}"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.525954084170477*^9, 3.525954226937791*^9}, { 3.526125728217949*^9, 3.526125827066271*^9}}], Cell[BoxData[ TagBox[GridBox[{ {"Symbol", "\<\"Meaning\"\>", "\<\"Shorthand reference\"\>", \ "\<\"Domain\"\>"}, {"\<\"f0\"\>", "\<\"probability of an insured event if the insured takes \ no care\"\>", "\<\"endowed risk\"\>", "\<\"(0,1)\"\>"}, {"\<\"k\"\>", "\<\"responsiveness to care of the probability of the \ insured event\"\>", "\<\"responsiveness\"\>", "\<\"(0,\[Infinity])\"\>"}, {"\<\"\[Phi]\"\>", "\<\"level of post-veil risk aversion\"\>", \ "\<\"post-veil risk aversion\"\>", "\<\"[0,1]\"\>"} }, AutoDelete->False, BaseStyle->{FontFamily -> "Swiss", FontSize -> 14}, GridBoxBackground->{"Columns" -> {{ RGBColor[ 0.9254901960784314, 0.8666666666666667, 0.7568627450980392]}}, "Rows" -> { RGBColor[0.7333333333333333, 0.6666666666666666, 0.5411764705882353]}}, GridBoxDividers->{"Columns" -> {{True}}, "Rows" -> {{True}}}, GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Grid"]], "Output", CellChangeTimes->{ 3.5259541012387857`*^9, {3.525954169149783*^9, 3.5259541824526997`*^9}, 3.52595422741888*^9, {3.5261257743065567`*^9, 3.526125827451337*^9}}] }, {2}]], Cell[CellGroupData[{ Cell[TextData[{ "Insurers cluster insureds into ", StyleBox["m", FontSlant->"Italic"], " categories according to a function of their perception of ", StyleBox["f0", FontSlant->"Italic"], " and ", StyleBox["k", FontSlant->"Italic"], ". The number of categories and methods of clustering may be restricted by \ law. Each cluster has n[\[ScriptC]] people in it where \[ScriptC] \ \[Element]{1..m}. Insurers offer members of each cluster a contract that has \ two features: a premium ", Cell[BoxData[ FormBox[ RowBox[{"(", SubscriptBox["\[CapitalPi]", "\[ScriptC]"]}], TraditionalForm]]], ") and a care condition ", Cell[BoxData[ FormBox[ RowBox[{"(", SubscriptBox["\[CapitalChi]", "\[ScriptC]"]}], TraditionalForm]]], "). The premium is defined as an amount per dollar that the insurer will \ have to pay in the event of an insured event. The care condition means that, \ if it is determined following an insured event that the insured failed to \ take \[CapitalChi] precautions, the insurer is excused from an otherwise \ existing duty to pay the claim. The insurer chooses \[CapitalChi] to be some \ quantile ", StyleBox["q", FontSlant->"Italic"], " of the levels of care the insurer perceives insureds in that cluster would \ take if there were no insurance available, the idea being to prevent \ inefficient moral hazard." }], "ItemNumbered", CellChangeTimes->{{3.52586679600169*^9, 3.525866909223736*^9}, { 3.5258669723032293`*^9, 3.525867034065905*^9}, {3.5258670964244223`*^9, 3.525867184972842*^9}, {3.525867396586287*^9, 3.5258673972837133`*^9}, { 3.525871399728538*^9, 3.525871433838801*^9}, 3.5258754493323717`*^9, { 3.525875686436966*^9, 3.525875779057291*^9}, {3.525954292420637*^9, 3.525954294064261*^9}, {3.527851955932294*^9, 3.5278519580649643`*^9}, { 3.527852131504692*^9, 3.527852228958371*^9}, {3.527933130944254*^9, 3.527933131097034*^9}}], Cell[TextData[{ "Given the contract {\[CapitalPi],\[CapitalChi]} available to members of \ their cluster, insureds in that cluster then choose a level of insurance (i \ \[Times] \[ScriptL]) to purchase and a level of care (x) to take. The law \ restricts the insured to purchase between ", Cell[BoxData[ FormBox[ SubscriptBox["i", "min"], TraditionalForm]]], " and ", Cell[BoxData[ FormBox[ SubscriptBox["i", "max"], TraditionalForm]]], " in insurance. The insured is assumed to optimize its behavior ", Cell[BoxData[ FormBox[ RowBox[{"{", RowBox[{ SuperscriptBox["i", "*"], ",", SuperscriptBox["x", "*"]}]}], TraditionalForm]]], "} based on its perception of its immutable characteristics ", Cell[BoxData[ FormBox[ SubscriptBox["\[ScriptCapitalF]", "d"], TraditionalForm]]], ":", Cell[BoxData[ FormBox[ RowBox[{"(", SubscriptBox["f", "d"]}], TraditionalForm]]], ",\[Phi],k) and the contract ", Cell[BoxData[ FormBox[ SubscriptBox["\[ScriptCapitalK]", "\[ScriptC]"], TraditionalForm]]], ":", Cell[BoxData[ FormBox[ RowBox[{"{", RowBox[{ SubscriptBox["\[CapitalPi]", "\[ScriptC]"], ",", SubscriptBox["\[CapitalChi]", "\[ScriptC]"]}]}], TraditionalForm]]], "} available to the insured. Thus, a long form of the ideal contract is" }], "ItemNumbered", CellChangeTimes->{{3.525867043465476*^9, 3.52586710038444*^9}, { 3.5258671911945553`*^9, 3.525867269686214*^9}, {3.525867442432417*^9, 3.5258674442776527`*^9}, {3.525871441207143*^9, 3.5258714622336073`*^9}, { 3.5258714935531883`*^9, 3.5258715041177673`*^9}, {3.5258754625160303`*^9, 3.52587548582615*^9}, {3.5258755619531*^9, 3.525875592274531*^9}, { 3.525876032442142*^9, 3.525876065809132*^9}, {3.527851982312324*^9, 3.527852006821419*^9}, {3.527852237335318*^9, 3.527852268229205*^9}, { 3.5279331551687317`*^9, 3.527933156768353*^9}, {3.5279338355769463`*^9, 3.527933898786024*^9}, {3.5279400043394327`*^9, 3.527940005186434*^9}}] }, Open ]], Cell[BoxData[ FormBox[ RowBox[{"{", RowBox[{ RowBox[{ SuperscriptBox["i", "*"], "[", RowBox[{ SubscriptBox["\[ScriptCapitalF]", "d"], ",", SubscriptBox["\[ScriptCapitalK]", "\[ScriptC]"]}], "]"}], ",", RowBox[{ SuperscriptBox["x", "*"], "[", RowBox[{ SubscriptBox["\[ScriptCapitalF]", "d"], ",", SubscriptBox["\[ScriptCapitalK]", "\[ScriptC]"]}], "]"}]}], "}"}], TraditionalForm]], "DisplayFormulaNumbered", CellChangeTimes->{{3.527933847502083*^9, 3.527933862050743*^9}, { 3.527933902607965*^9, 3.5279339417611933`*^9}}], Cell[TextData[{ "The contract that is offered by the insurer to members of each cluster in \ turn attempts to be \[OpenCurlyDoubleQuote]an equilibrium contract;\ \[CloseCurlyDoubleQuote] one in which, given the ", Cell[BoxData[ FormBox[ RowBox[{"{", RowBox[{ SuperscriptBox["i", "*"], ",", SuperscriptBox["x", "*"]}]}], TraditionalForm]]], "} choices that would result from the members of the cluster, the insurer \ would break even. " }], "ItemNumbered", CellChangeTimes->{{3.525867284690301*^9, 3.525867331245861*^9}, { 3.525867447044883*^9, 3.5258674477084303`*^9}, {3.5258756200051107`*^9, 3.5258756471619873`*^9}, {3.5258760755188837`*^9, 3.5258760911670856`*^9}, { 3.527779979286628*^9, 3.527780230166855*^9}, {3.5278520289829597`*^9, 3.5278520919489107`*^9}, {3.527852977725918*^9, 3.5278529823634872`*^9}, { 3.527933180470791*^9, 3.5279331880787067`*^9}, {3.527933377671527*^9, 3.527933378422978*^9}}], Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ RowBox[{ SubscriptBox["\[ForAll]", RowBox[{"\[ScriptC]", "\[Element]", RowBox[{"{", RowBox[{ RowBox[{"1", ".."}], "m"}], "}"}]}]], RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"j", "=", "1"}], RowBox[{"n", "[", "\[ScriptC]", "]"}]], RowBox[{ SubscriptBox[ RowBox[{"(", SuperscriptBox["\[ScriptCapitalE]", "*"], ")"}], "j"], SubscriptBox[ RowBox[{"(", SuperscriptBox["i", "*"], ")"}], "j"], SubscriptBox["\[ScriptL]", "j"]}]}]}], "=", RowBox[{ RowBox[{"(", RowBox[{"1", "+", 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An auxiliary variable ", Cell[BoxData[ FormBox["q", TraditionalForm]]], " is used in this process. The initial guess is based on a user-specified \ premium (often zero) and a user-specified quantile ", StyleBox["q0", FontSlant->"Italic"], " of the levels of care that would be taken by members of the cluster if \ there were no insurance. 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= 0.01, $CellContext`kmax$$ = 20, $CellContext`k\[Epsilon]$$ = 0.1, $CellContext`k\[Mu]$$ = 0.5, $CellContext`popSize$$ = 20, $CellContext`populationVisualization$$ = "Grid", $CellContext`xcharacteristic$$ = "f\[Alpha]", $CellContext`ycharacteristic$$ = "f\[Alpha]", $CellContext`zcharacteristic$$ = "f\[Alpha]", $CellContext`\[ScriptL]$$ = 1, $CellContext`\[Epsilon]$$ = 0.1, $CellContext`\[Mu]$$ = 0.2, $CellContext`\[Phi]\[Epsilon]$$ = 0.1, $CellContext`\[Phi]\[Mu]$$ = 0.5}, "ControllerVariables" :> { Hold[$CellContext`popSize$$, $CellContext`popSize$53598$$, 0], Hold[$CellContext`\[Mu]$$, $CellContext`\[Mu]$53599$$, 0], Hold[$CellContext`\[Epsilon]$$, $CellContext`\[Epsilon]$53600$$, 0], Hold[$CellContext`\[ScriptL]$$, $CellContext`\[ScriptL]$53601$$, 0], Hold[$CellContext`\[Phi]\[Mu]$$, $CellContext`\[Phi]\[Mu]$53602$$, 0], Hold[$CellContext`\[Phi]\[Epsilon]$$, \ $CellContext`\[Phi]\[Epsilon]$53603$$, 0], Hold[$CellContext`kmax$$, $CellContext`kmax$53604$$, 0], Hold[$CellContext`k\[Mu]$$, $CellContext`k\[Mu]$53605$$, 0], Hold[$CellContext`k\[Epsilon]$$, $CellContext`k\[Epsilon]$53606$$, 0], Hold[$CellContext`insuredBias$$, $CellContext`insuredBias$53607$$, 0], Hold[$CellContext`characteristic$$, \ $CellContext`characteristic$53608$$, False], Hold[$CellContext`xcharacteristic$$, \ $CellContext`xcharacteristic$53609$$, False], Hold[$CellContext`ycharacteristic$$, \ $CellContext`ycharacteristic$53610$$, False], Hold[$CellContext`zcharacteristic$$, \ $CellContext`zcharacteristic$53611$$, False]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Row[{ Pane[{ Dynamic[$CellContext`f\[Delta] = RandomVariate[ $CellContext`scaledBetaDistribution[$CellContext`\[Mu]$$, \ $CellContext`\[Epsilon]$$], {$CellContext`popSize$$}], TrackedSymbols :> {$CellContext`popSize$$, $CellContext`\[Mu]$$, \ $CellContext`\[Epsilon]$$}], Dynamic[$CellContext`\[ScriptL]\[Delta] = RandomVariate[ TransformedDistribution[$CellContext`\[ScriptL]$$ \ $CellContext`loss, Distributed[$CellContext`loss, BernoulliDistribution[1]]], {$CellContext`popSize$$}], TrackedSymbols :> {$CellContext`popSize$$, \ $CellContext`\[ScriptL]$$}], Dynamic[$CellContext`\[Phi]\[Delta] = RandomVariate[ $CellContext`scaledBetaDistribution[$CellContext`\[Phi]\[Mu]$$, \ $CellContext`\[Phi]\[Epsilon]$$], {$CellContext`popSize$$}], TrackedSymbols :> {$CellContext`popSize$$, $CellContext`\[Phi]\ \[Mu]$$, $CellContext`\[Phi]\[Epsilon]$$}], Dynamic[$CellContext`k\[Delta] = RandomVariate[ TransformedDistribution[$CellContext`kmax$$ $CellContext`b, Distributed[$CellContext`b, $CellContext`scaledBetaDistribution[$CellContext`k\[Mu]$$, \ $CellContext`k\[Epsilon]$$]]], {$CellContext`popSize$$}], TrackedSymbols :> {$CellContext`popSize$$, $CellContext`kmax$$, \ $CellContext`k\[Mu]$$, $CellContext`k\[Epsilon]$$}], Dynamic[$CellContext`fd\[Delta] = Map[RandomVariate[ $CellContext`perceptionDistribution[#, \ $CellContext`insuredBias$$, $CellContext`insuredDispersion$$]]& , \ $CellContext`f\[Delta]], TrackedSymbols :> {$CellContext`popSize$$, \ $CellContext`f\[Delta], $CellContext`\[Mu]$$, $CellContext`\[Epsilon]$$, \ $CellContext`insuredBias$$, $CellContext`insuredDispersion$$}], Dynamic[$CellContext`fr\[Delta] = Map[RandomVariate[ $CellContext`perceptionDistribution[#, \ $CellContext`insurerBias$$, $CellContext`insurerDispersion$$]]& , \ $CellContext`f\[Delta]], TrackedSymbols :> {$CellContext`popSize$$, \ $CellContext`f\[Delta], $CellContext`\[Mu]$$, $CellContext`\[Epsilon]$$, \ $CellContext`insurerBias$$, $CellContext`insurerDispersion$$}], Dynamic[$CellContext`\[ScriptCapitalP] = Transpose[{$CellContext`f\[Delta], $CellContext`fd\[Delta], \ $CellContext`fr\[Delta], $CellContext`\[ScriptL]\[Delta], $CellContext`\[Phi]\ \[Delta], $CellContext`k\[Delta]}]]}, ImageSize -> {1, 1}, BaseStyle -> (ShowContents -> False)], Dynamic[ Pane[ Module[{$CellContext`characteristicToIndex$ = { "f\[Alpha]" -> 1, "fd" -> 2, "fr" -> 3, "\[ScriptL]" -> 4, "\[Phi]" -> 5, "k" -> 6}, $CellContext`minRules$ = { "f\[Alpha]" -> 0, "fd" -> 0, "fr" -> 0, "\[ScriptL]" -> 0, "\[Phi]" -> 0, "k" -> 0}, $CellContext`maxRules$ = { "f\[Alpha]" -> 1, "fd" -> 1, "fr" -> 1, "\[ScriptL]" -> 10, "\[Phi]" -> 1, "k" -> 50}, $CellContext`cosmetics$ = { ImageSize -> {400, 400}, ImagePadding -> {{60, 10}, {60, 10}}, BaseStyle -> { FontFamily -> "Swiss", FontSize -> 12}}, $CellContext`cosmetics2D$, \ $CellContext`cosmeticsHistogram$, $CellContext`cosmetics3D$, \ $CellContext`cosmeticsHistogram3D$}, $CellContext`cosmetics2D$ = { Axes -> False, Frame -> True, FrameLabel -> {$CellContext`xcharacteristic$$, \ $CellContext`ycharacteristic$$}, PlotRange -> { Map[Rescale[#, {0, 1}, { ReplaceAll[$CellContext`xcharacteristic$$, \ $CellContext`minRules$], ReplaceAll[$CellContext`xcharacteristic$$, \ $CellContext`maxRules$]}]& , {0, 1}], Map[Rescale[#, {0, 1}, { ReplaceAll[$CellContext`ycharacteristic$$, \ $CellContext`minRules$], ReplaceAll[$CellContext`ycharacteristic$$, \ $CellContext`maxRules$]}]& , {0, 1}]}}; $CellContext`cosmeticsHistogram$ = { Axes -> False, Frame -> True, FrameLabel -> {$CellContext`characteristic$$, "Count"}}; $CellContext`cosmeticsHistogram3D$ = { AxesLabel -> {$CellContext`xcharacteristic$$, \ $CellContext`ycharacteristic$$, "Count"}}; $CellContext`cosmetics3D$ = FilterRules[{PlotStyle -> PointSize[0.02], PlotRange -> { Map[Rescale[#, {0, 1}, { ReplaceAll[$CellContext`xcharacteristic$$, \ $CellContext`minRules$], ReplaceAll[$CellContext`xcharacteristic$$, \ $CellContext`maxRules$]}]& , {0, 1}], Map[Rescale[#, {0, 1}, { ReplaceAll[$CellContext`ycharacteristic$$, \ $CellContext`minRules$], ReplaceAll[$CellContext`ycharacteristic$$, \ $CellContext`maxRules$]}]& , {0, 1}], Map[Rescale[#, {0, 1}, { ReplaceAll[$CellContext`zcharacteristic$$, \ $CellContext`minRules$], ReplaceAll[$CellContext`zcharacteristic$$, \ $CellContext`maxRules$]}]& , {0, 1}]}, AxesLabel -> {$CellContext`xcharacteristic$$, \ $CellContext`ycharacteristic$$, $CellContext`zcharacteristic$$}}, Options[ Switch[$CellContext`populationVisualization$$, "Histogram", Histogram, "Histogram3D", Histogram3D, "ListPlot", ListPlot, "ListPointPlot3D", ListPointPlot3D]]]; Switch[$CellContext`populationVisualization$$, "Grid", Grid[ ReplaceAll[ Join[{{"true risk", "insured perceived risk", "insurer perceived risk", "loss", "risk aversion", "responsiveness"}, { "f\[Alpha]", "fd", "fr", "\[ScriptL]", "\[Phi]", "k"}}, $CellContext`\[ScriptCapitalP]], PatternTest[ Pattern[$CellContext`x, Blank[Real]], NumericQ] :> NumberForm[$CellContext`x, {5, 3}]], BaseStyle -> { LineIndent -> 0, FontFamily -> "Swiss", FontSize -> 12, FontColor -> White}, Dividers -> All, Alignment -> Left, Background -> With[{$CellContext`palette = 35}, { None, {$CellContext`myRed, $CellContext`mySeaFoam, { ColorData[$CellContext`palette][5], ColorData[$CellContext`palette][6]}}}], ItemSize -> {{6., 6., 6., 3.3, 6., 6.}, 1}], "Histogram", Histogram[ Part[$CellContext`\[ScriptCapitalP], All, ReplaceAll[$CellContext`characteristic$$, \ $CellContext`characteristicToIndex$]], Evaluate[ Apply[Sequence, $CellContext`cosmetics$]], Evaluate[ Apply[Sequence, $CellContext`cosmeticsHistogram$]]], "Histogram3D", Histogram3D[ Part[$CellContext`\[ScriptCapitalP], All, ReplaceAll[{$CellContext`xcharacteristic$$, \ $CellContext`ycharacteristic$$}, $CellContext`characteristicToIndex$]], Evaluate[ Apply[Sequence, $CellContext`cosmetics$]], Evaluate[ Apply[Sequence, $CellContext`cosmeticsHistogram3D$]]], "ListPlot", ListPlot[ Part[$CellContext`\[ScriptCapitalP], All, ReplaceAll[{$CellContext`xcharacteristic$$, \ $CellContext`ycharacteristic$$}, $CellContext`characteristicToIndex$]], Evaluate[ Apply[Sequence, $CellContext`cosmetics$]], Evaluate[ Apply[Sequence, $CellContext`cosmetics2D$]]], "ListPointPlot3D", ListPointPlot3D[ Part[$CellContext`\[ScriptCapitalP], All, ReplaceAll[{$CellContext`xcharacteristic$$, \ $CellContext`ycharacteristic$$, $CellContext`zcharacteristic$$}, \ $CellContext`characteristicToIndex$]], Evaluate[ Apply[Sequence, $CellContext`cosmetics$]], Evaluate[ Apply[Sequence, $CellContext`cosmetics3D$]]]]], {425, 400}, Scrollbars -> {True, True}]]}], "Specifications" :> {{{$CellContext`popSize$$, 20, "population size (n)"}, 5, 200, 5, Appearance -> "Labeled", ImageSize -> Small, ControlPlacement -> 1}, {{$CellContext`\[Mu]$$, 0.2, "mean f0 (\[Mu])"}, 0.01, 0.99, 0.01, Appearance -> "Labeled", ImageSize -> Small, ControlPlacement -> 2}, {{$CellContext`\[Epsilon]$$, 0.1, "f0 dispersion (\[Epsilon])"}, 0.01, 0.99, 0.01, Appearance -> "Labeled", ImageSize -> Small, ControlPlacement -> 3}, {{$CellContext`\[ScriptL]$$, 1, "loss (\[ScriptL]}"}, 1, 10, 0.1, Appearance -> "Labeled", ImageSize -> Small, ControlPlacement -> 4}, {{$CellContext`\[Phi]\[Mu]$$, 0.5, "mean risk aversion (\[Phi]\[Mu])"}, 0.01, 0.99, 0.01, Appearance -> "Labeled", ImageSize -> Small, ControlPlacement -> 5}, {{$CellContext`\[Phi]\[Epsilon]$$, 0.1, "risk aversion dispersion (\[Phi]\[Epsilon])"}, 0.01, 0.99, 0.01, Appearance -> "Labeled", ImageSize -> Small, ControlPlacement -> 6}, {{$CellContext`kmax$$, 20, "maximum resp. (\!\(\*SubscriptBox[\(k\), \(max\)]\))"}, 0.1, 50, 0.1, Appearance -> "Labeled", ImageSize -> Small, ControlPlacement -> 7}, {{$CellContext`k\[Mu]$$, 0.5, "mean/max. resp. (k\[Mu])"}, 0.01, 0.99, 0.01, Appearance -> "Labeled", ImageSize -> Small, ControlPlacement -> 8}, {{$CellContext`k\[Epsilon]$$, 0.1, "resp. dispersion (k\[Epsilon])"}, 0.01, 0.99, 0.01, Appearance -> "Labeled", ImageSize -> Small, ControlPlacement -> 9}, {{$CellContext`insuredBias$$, 0, "insured bias (d\[ScriptB])"}, -0.9, 0.9, 0.01, Appearance -> "Labeled", ImageSize -> Small, ControlPlacement -> 10}, {{$CellContext`insuredDispersion$$, 0.01, "insured dispersion (d\[Epsilon])"}, 0.01, 0.99, 0.01, Appearance -> "Labeled", ImageSize -> Small, ControlPlacement -> 11}, {{$CellContext`insurerBias$$, 0, "insurer bias (r\[ScriptB])"}, -0.9, 0.9, 0.01, Appearance -> "Labeled", ImageSize -> Small, ControlPlacement -> 12}, {{$CellContext`insurerDispersion$$, 0.01, "insurer dispersion (r\[Epsilon])"}, 0.01, 0.99, 0.01, Appearance -> "Labeled", ImageSize -> Small, ControlPlacement -> 13}, Column[{ Style["population parameters", 14, FontSlant -> "Italic"], Manipulate`Place[1], Manipulate`Place[2], Manipulate`Place[3], Manipulate`Place[4], Manipulate`Place[5], Manipulate`Place[6], Manipulate`Place[7], Manipulate`Place[8], Manipulate`Place[9], Manipulate`Place[10], Manipulate`Place[11], Manipulate`Place[12], Manipulate`Place[13]}], Delimiter, Style[ "visualization", 14, FontSlant -> "Italic"], {{$CellContext`populationVisualization$$, "Grid", "population visualization"}, { "Grid", "Histogram", "Histogram3D", "ListPlot", "ListPointPlot3D"}, ControlType -> PopupMenu}, {{$CellContext`characteristic$$, "f\[Alpha]", "characteristic"}, { "f\[Alpha]" -> "true risk (f\[Alpha])", "fd" -> "insured perceived risk (fd)", "fr" -> "insurer perceived risk (fr)", "\[ScriptL]" -> "loss (\[ScriptL])", "\[Phi]" -> "risk aversion (\[Phi])", "k" -> "responsiveness (k)"}, ControlPlacement -> 14}, {{$CellContext`xcharacteristic$$, "f\[Alpha]", "x-characteristic"}, { "f\[Alpha]" -> "true risk (f\[Alpha])", "fd" -> "insured perceived risk (fd)", "fr" -> "insurer perceived risk (fr)", "\[ScriptL]" -> "loss (\[ScriptL])", "\[Phi]" -> "risk aversion (\[Phi])", "k" -> "responsiveness (k)"}, ControlPlacement -> 15}, {{$CellContext`ycharacteristic$$, "f\[Alpha]", "y-characteristic"}, { "f\[Alpha]" -> "true risk (f\[Alpha])", "fd" -> "insured perceived risk (fd)", "fr" -> "insurer perceived risk (fr)", "\[ScriptL]" -> "loss (\[ScriptL])", "\[Phi]" -> "risk aversion (\[Phi])", "k" -> "responsiveness (k)"}, ControlPlacement -> 16}, {{$CellContext`xcharacteristic$$, "f\[Alpha]", "x-characteristic"}, { "f\[Alpha]" -> "true risk (f\[Alpha])", "fd" -> "insured perceived risk (fd)", "fr" -> "insurer perceived risk (fr)", "\[ScriptL]" -> "loss (\[ScriptL])", "\[Phi]" -> "risk aversion (\[Phi])", "k" -> "responsiveness (k)"}, ControlPlacement -> 17}, {{$CellContext`ycharacteristic$$, "f\[Alpha]", "y-characteristic"}, { "f\[Alpha]" -> "true risk (f\[Alpha])", "fd" -> "insured perceived risk (fd)", "fr" -> "insurer perceived risk (fr)", "\[ScriptL]" -> "loss (\[ScriptL])", "\[Phi]" -> "risk aversion (\[Phi])", "k" -> "responsiveness (k)"}, ControlPlacement -> 18}, {{$CellContext`xcharacteristic$$, "f\[Alpha]", "x-characteristic"}, { "f\[Alpha]" -> "true risk (f\[Alpha])", "fd" -> "insured perceived risk (fd)", "fr" -> "insurer perceived risk (fr)", "\[ScriptL]" -> "loss (\[ScriptL])", "\[Phi]" -> "risk aversion (\[Phi])", "k" -> "responsiveness (k)"}, ControlPlacement -> 19}, {{$CellContext`ycharacteristic$$, "f\[Alpha]", "y-characteristic"}, { "f\[Alpha]" -> "true risk (f\[Alpha])", "fd" -> "insured perceived risk (fd)", "fr" -> "insurer perceived risk (fr)", "\[ScriptL]" -> "loss (\[ScriptL])", "\[Phi]" -> "risk aversion (\[Phi])", "k" -> "responsiveness (k)"}, ControlPlacement -> 20}, {{$CellContext`zcharacteristic$$, "f\[Alpha]", "z-characteristic"}, { "f\[Alpha]" -> "true risk (f\[Alpha])", "fd" -> "insured perceived risk (fd)", "fr" -> "insurer perceived risk (fr)", "\[ScriptL]" -> "loss (\[ScriptL])", "\[Phi]" -> "risk aversion (\[Phi])", "k" -> "responsiveness (k)"}, ControlPlacement -> 21}, PaneSelector[{ "Grid" -> "", "Histogram" -> Manipulate`Place[14], "Histogram3D" -> Column[{ Manipulate`Place[15], Spacer[24], Manipulate`Place[16]}], "ListPlot" -> Column[{ Manipulate`Place[17], Spacer[24], Manipulate`Place[18]}], "ListPointPlot3D" -> Column[{ Manipulate`Place[19], Spacer[24], Manipulate`Place[20], Spacer[24], Manipulate`Place[21]}]}, Dynamic[$CellContext`populationVisualization$$]]}, "Options" :> { ControlPlacement -> Left, LabelStyle -> {FontSize -> 12, FontFamily -> "Swiss", RGBColor[ 0.8156862745098039, 0.07058823529411765, 0.07058823529411765]}}, "DefaultOptions" :> {}], ImageSizeCache->{799., {267., 274.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{ 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Cell["\<\ In general, just adjust the premium to the value which, if care remained \ unchanged, would cause the insurer to just break even. If, however, the \ system \"blows up,\[CloseCurlyDoubleQuote] search \ {\[CapitalPi],\[CapitalChi]} space through a hemi-boustrophedonic algorithm \ in which the premium is cut in half, the care condition is adjusted to a \ user-specified fraction of the current quantile of the existing distribution \ of care, and the current quantile is adjusted to a user-specified fraction of \ the current quantile\ \>", "ItemNumbered", CellChangeTimes->{{3.527677271031116*^9, 3.5276774813305197`*^9}, 3.5281255263845263`*^9}], Cell["\<\ Programming idea similar to that in many New Kind of Science dynamical systems\ \>", "ItemNumbered", CellChangeTimes->{{3.527597051817821*^9, 3.527597076039104*^9}, { 3.527676183826914*^9, 3.527676184771439*^9}, {3.5276762813867207`*^9, 3.527676298205839*^9}}], Cell["use an uncompiled function for each iteration", "SubitemNumbered", CellChangeTimes->{{3.527676192123908*^9, 3.527676206954632*^9}, { 3.527676257053887*^9, 3.527676259966741*^9}}] }, Open ]], Cell[BoxData[ 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\[Lambda]_, ibounds : {imin_, imax_}, ixmFunction_, payoutBasis_, \ behaviorBasis_, quantileAdjustmentAlgorithmFactory_, \ quantileAdjustmentParameter_, fixedPointIters_Integer] := \ FixedPointList[contractEquilibrateStep[\[ScriptCapitalP], #1, \[Rho], \ \[Lambda], ibounds, ixmFunction, payoutBasis, behaviorBasis, \ quantileAdjustmentAlgorithmFactory, quantileAdjustmentParameter] &, {\ \[CapitalPi], \[CapitalChi], q}, fixedPointIters]\ \>", "ProgramNumbered", GeneratedCell->False, CellAutoOverwrite->False, CellChangeTimes->{{3.527588385123981*^9, 3.527588469677533*^9}, 3.52758936458709*^9, {3.527591444014845*^9, 3.527591472683666*^9}, { 3.5275923116930532`*^9, 3.5275923141170692`*^9}, {3.5275923508269167`*^9, 3.527592397660925*^9}, {3.527594354991983*^9, 3.527594375781864*^9}, 3.527597181820623*^9, {3.527597473050737*^9, 3.5275974767135878`*^9}}], Cell["\<\ contractTrajectoryC[\[ScriptCapitalP]_, {\[CapitalPi]_, \[CapitalChi]_, q_}, \ \[Rho]_, \[Lambda]_, ibounds : {imin_, imax_}, 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Manipulate`Place[24], Manipulate`Place[25], Manipulate`Place[26], Grid[{{ Manipulate`Place[27], Manipulate`Place[28]}, { Manipulate`Place[29], Manipulate`Place[30]}}]}], "traditional" -> Column[{ Grid[{{ Manipulate`Place[31], Manipulate`Place[32]}, { Manipulate`Place[33], Manipulate`Place[34]}}], Manipulate`Place[35], Manipulate`Place[36], Manipulate`Place[37], Manipulate`Place[38], Row[{ Manipulate`Place[39], Manipulate`Place[40]}], Row[{ Manipulate`Place[41], Spacer[18], Manipulate`Place[42]}], Manipulate`Place[43]}]}, Dynamic[$CellContext`tab$$]]}]}], 368]], Manipulate`Dump`ThisIsNotAControl}}, Typeset`size$$ = { 380., {226., 234.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = True, $CellContext`\[CapitalEta]$84845$$ = 0, $CellContext`fpiters$84846$$ = 0, $CellContext`safetyQuantile$84847$$ = 0, $CellContext`\[CapitalPi]0$84848$$ = 0, $CellContext`q0Control$84849$$ = 0, $CellContext`quantileAdjustmentFactor$84850$$ = 0, $CellContext`m1$84851$$ = 0, $CellContext`m2$84852$$ = 0, $CellContext`\[Rho]$84853$$ = 0, $CellContext`loadBasis$84854$$ = False, $CellContext`\[Lambda]direct$84855$$ = 0, $CellContext`show\[ScriptCapitalS]$84856$$ = False, $CellContext`histogramLayout$84857$$ = False, $CellContext`xBasis$84858$$ = False}, DynamicBox[Manipulate`ManipulateBoxes[ 2, StandardForm, "Variables" :> {$CellContext`clusterStatisticsPalette$$ = 35, $CellContext`f0Basis$$ = "true", $CellContext`firstPointDirectives$$ = "nothing special", $CellContext`fpiters$$ = 0, $CellContext`histogramLayout$$ = "Stacked", $CellContext`histogramPalette$$ = 35, $CellContext`imax$$ = 1, $CellContext`imin$$ = 0, $CellContext`loadBasis$$ = "direct", $CellContext`m1$$ = 1, $CellContext`m2$$ = 1, $CellContext`pointSizeBasis$$ = "insurance", $CellContext`q0Control$$ = 0.25, $CellContext`quantileAdjustmentFactor$$ = 0.7, $CellContext`safetyQuantile$$ = 0.5, $CellContext`showConditions$$ = False, $CellContext`showCoverageRamps$$ = False, $CellContext`showInsureds$$ = True, $CellContext`showPremiumLines$$ = True, $CellContext`show\[ScriptCapitalS]$$ = True, $CellContext`tab$$ = "traditional", $CellContext`trajectoryColorPalette$$ = 35, $CellContext`trajectoryShow$$ = "strong", $CellContext`v1$$ = 1, $CellContext`v2$$ = 1, $CellContext`xBasis$$ = "acc. prob.", $CellContext`xhighControl$$ = 1, $CellContext`xlowControl$$ = 0, $CellContext`yBasis$$ = "risk aversion", $CellContext`yhighControl$$ = 1, $CellContext`ylowControl$$ = 0, $CellContext`\[CapitalEta]$$ = 0, $CellContext`\[Lambda]0$$ = 0, $CellContext`\[Lambda]cc$$ = 0, $CellContext`\[Lambda]direct$$ = 0, $CellContext`\[Lambda]Multiply$$ = False, $CellContext`\[Lambda]\[Rho]$$ = 0, $CellContext`\[CapitalPi]0$$ = 0, $CellContext`\[Rho]$$ = 0.1}, "ControllerVariables" :> { Hold[$CellContext`\[CapitalEta]$$, $CellContext`\[CapitalEta]$84845$$, 0], Hold[$CellContext`fpiters$$, $CellContext`fpiters$84846$$, 0], Hold[$CellContext`safetyQuantile$$, \ $CellContext`safetyQuantile$84847$$, 0], Hold[$CellContext`\[CapitalPi]0$$, $CellContext`\[CapitalPi]0$84848$$, 0], Hold[$CellContext`q0Control$$, $CellContext`q0Control$84849$$, 0], Hold[$CellContext`quantileAdjustmentFactor$$, \ $CellContext`quantileAdjustmentFactor$84850$$, 0], Hold[$CellContext`m1$$, $CellContext`m1$84851$$, 0], Hold[$CellContext`m2$$, $CellContext`m2$84852$$, 0], Hold[$CellContext`\[Rho]$$, $CellContext`\[Rho]$84853$$, 0], Hold[$CellContext`loadBasis$$, $CellContext`loadBasis$84854$$, False], Hold[$CellContext`\[Lambda]direct$$, \ $CellContext`\[Lambda]direct$84855$$, 0], Hold[$CellContext`show\[ScriptCapitalS]$$, $CellContext`show\ \[ScriptCapitalS]$84856$$, False], Hold[$CellContext`histogramLayout$$, \ $CellContext`histogramLayout$84857$$, False], Hold[$CellContext`xBasis$$, $CellContext`xBasis$84858$$, False]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Dynamic[ $CellContext`insuranceSystem[$CellContext`clusterStatisticsPalette$$, $CellContext`f0Basis$$, $CellContext`firstPointDirectives$$, \ $CellContext`fpiters$$, $CellContext`histogramLayout$$, \ $CellContext`histogramPalette$$, $CellContext`imax$$, $CellContext`imin$$, \ $CellContext`loadBasis$$, $CellContext`m1$$, $CellContext`m2$$, \ $CellContext`pointSizeBasis$$, $CellContext`q0Control$$, \ $CellContext`quantileAdjustmentFactor$$, $CellContext`safetyQuantile$$, \ $CellContext`showConditions$$, $CellContext`showCoverageRamps$$, \ $CellContext`showInsureds$$, $CellContext`showPremiumLines$$, \ $CellContext`show\[ScriptCapitalS]$$, $CellContext`tab$$, \ $CellContext`trajectoryColorPalette$$, $CellContext`trajectoryShow$$, \ $CellContext`v1$$, $CellContext`v2$$, $CellContext`xBasis$$, \ $CellContext`xhighControl$$, $CellContext`xlowControl$$, \ $CellContext`yBasis$$, $CellContext`yhighControl$$, \ $CellContext`ylowControl$$, $CellContext`\[CapitalEta]$$, $CellContext`\ \[Lambda]0$$, $CellContext`\[Lambda]cc0, $CellContext`\[Lambda]direct$$, \ $CellContext`\[Lambda]Multiply$$, $CellContext`\[Lambda]\[Rho]$$, \ $CellContext`\[CapitalPi]0$$, $CellContext`\[Rho]$$]], "Specifications" :> {{{$CellContext`\[CapitalEta]$$, 0, "behind the veil risk aversion (\[CapitalEta])"}, 0, 5, 0.1, Appearance -> "Labeled", ImageSize -> Small}, {{$CellContext`fpiters$$, 0, "fixed point list iterations"}, 0, 20, 1, Appearance -> "Labeled", ImageSize -> Small}, {{$CellContext`safetyQuantile$$, 0.5, "safety quantile"}, 0.1, 0.9, 0.1, Appearance -> "Labeled", ImageSize -> Small, ControlPlacement -> 1}, {{$CellContext`\[CapitalPi]0$$, 0, "initial premium"}, 0, 1, 0.01, ImageSize -> Small, Appearance -> "Labeled", ControlPlacement -> 2}, {{$CellContext`q0Control$$, 0.25, "quantile"}, 0, 1, 0.01, ImageSize -> Small, ControlPlacement -> 3}, {{$CellContext`quantileAdjustmentFactor$$, 0.7, "quantile adjustment factor"}, 0.01, 0.99, 0.01, Appearance -> "Labeled", ImageSize -> Small, ControlPlacement -> 4}, Pane[ OpenerView[{"advanced system evolution controls", Column[{ Manipulate`Place[1], Manipulate`Place[2], Row[{ Manipulate`Place[3], Spacer[10], Dynamic[ Round[ Rescale[$CellContext`q0Control$$, {0, 1}, {0.01, 1}], 0.01]]}], Manipulate`Place[4]}]}], 368], Delimiter, {{$CellContext`m1$$, 1, "premium clusters"}, {1, 2, 3, 4}, ControlPlacement -> 5}, {{$CellContext`m2$$, 1, "care condition clusters"}, {1, 2, 3}, ControlPlacement -> 6}, Pane[ OpenerView[{"clustering", Column[{ Manipulate`Place[5], Manipulate`Place[6]}]}], 400], Delimiter, {{$CellContext`\[Rho]$$, 0.1, "condition radius (\[Rho])"}, 0.01, 0.3, 0.01, Appearance -> "Labeled", ImageSize -> Small, ControlPlacement -> 7}, {{$CellContext`loadBasis$$, "direct", "load calculation method"}, {"direct", "parametric"}, ControlPlacement -> 8}, {{$CellContext`\[Lambda]direct$$, 0, "direct load"}, -0.9, 1, 0.01, Appearance -> "Labeled", ImageSize -> Small, ControlPlacement -> 9}, {{$CellContext`\[Lambda]0$$, 0, "baseline load"}, -0.9, 1, 0.01, Appearance -> "Labeled", ImageSize -> Small, ControlPlacement -> 10}, {{$CellContext`\[Lambda]cc$$, 0, "cluster count coefficient"}, -0.2, 0.2, 0.005, Appearance -> "Labeled", ImageSize -> Small, ControlPlacement -> 11}, {{$CellContext`\[Lambda]\[Rho]$$, 0, "\[Rho] coefficient"}, -0.9, 1, 0.01, Appearance -> "Labeled", ImageSize -> Small, ControlPlacement -> 12}, {{$CellContext`imin$$, 0, "minimum permitted insurance"}, 0, 0.9, 0.1, Appearance -> "Labeled", ImageSize -> Small, ControlPlacement -> 13}, {{$CellContext`imax$$, 1, "maximum permitted insurance"}, 0.1, 1, 0.1, Appearance -> "Labeled", ImageSize -> Small, ControlPlacement -> 14}, Pane[ OpenerView[{"regulatory", Column[{ Manipulate`Place[7], Manipulate`Place[8], PaneSelector[{"direct" -> Column[{ Manipulate`Place[9]}], "parametric" -> Row[{ Column[{ Manipulate`Place[10], Manipulate`Place[11], Manipulate`Place[12]}], "\[Lambda]:", Spacer[6], Dynamic[$CellContext`\[Lambda]0$$ + \ $CellContext`\[Lambda]cc$$ ($CellContext`m1$$ $CellContext`m2$$ - 1) + $CellContext`\[Lambda]\[Rho]$$ \ $CellContext`\[Rho]$$]}]}, Dynamic[$CellContext`loadBasis$$]], Manipulate`Place[13], Manipulate`Place[14]}]}], 368], Delimiter, {{$CellContext`show\[ScriptCapitalS]$$, True, "show behind-the-veil spectral measure"}, {True, False}, ControlPlacement -> 15}, {{$CellContext`tab$$, "traditional", "visualization"}, { "cluster statistics", "traditional", "histogram", "grid", "trajectory", "raw"}, ControlType -> PopupMenu, ControlPlacement -> 16}, {{$CellContext`v1$$, 1, "accident frequency cluster"}, Dynamic[ Range[$CellContext`m1$$]], ControlType -> SetterBar, ControlPlacement -> 17}, {{$CellContext`v2$$, 1, "care condition cluster"}, Dynamic[ Range[$CellContext`m2$$]], ControlType -> SetterBar, ControlPlacement -> 18}, {{$CellContext`clusterStatisticsPalette$$, 35, "palette"}, 1, 62, 1, ImageSize -> Small, Appearance -> "Labeled", ControlPlacement -> 19}, {{$CellContext`histogramPalette$$, 35, "palette index"}, 1, 62, 1, ImageSize -> Small, Appearance -> "Labeled", ControlPlacement -> 20}, {{$CellContext`histogramLayout$$, "Stacked", "layout"}, { "Stacked", "Overlapped"}, ControlPlacement -> 21}, {{$CellContext`v1$$, 1, "accident frequency cluster"}, Dynamic[ Range[$CellContext`m1$$]], ControlType -> SetterBar, ControlPlacement -> 22}, {{$CellContext`v2$$, 1, "care condition cluster"}, Dynamic[ Range[$CellContext`m2$$]], ControlType -> SetterBar, ControlPlacement -> 23}, {{$CellContext`trajectoryShow$$, "strong", "show trajectory how?"}, {"strong", "weak", "none"}, ControlPlacement -> 24}, {{$CellContext`firstPointDirectives$$, "nothing special", "initialization directive"}, { "nothing special", "large", "large and color by end point"}, ControlType -> PopupMenu, ControlPlacement -> 25}, {{$CellContext`trajectoryColorPalette$$, 35, "trajectory color palette index"}, 1, 62, 1, Appearance -> "Labeled", ImageSize -> Small, ControlPlacement -> 26}, {{$CellContext`xlowControl$$, 0, "x low"}, 0, 1, ImageSize -> Tiny, ControlPlacement -> 27}, {{$CellContext`xhighControl$$, 1, "x high"}, 0, 1, ImageSize -> Tiny, ControlPlacement -> 28}, {{$CellContext`ylowControl$$, 0, "y low"}, 0, 1, ImageSize -> Tiny, ControlPlacement -> 29}, {{$CellContext`yhighControl$$, 1, "y high"}, 0, 1, ImageSize -> Tiny, ControlPlacement -> 30}, {{$CellContext`xlowControl$$, 0, "x low"}, 0, 1, ImageSize -> Tiny, ControlPlacement -> 31}, {{$CellContext`xhighControl$$, 1, "x high"}, 0, 1, ImageSize -> Tiny, ControlPlacement -> 32}, {{$CellContext`ylowControl$$, 0, "y low"}, 0, 1, ImageSize -> Tiny, ControlPlacement -> 33}, {{$CellContext`yhighControl$$, 1, "y high"}, 0, 1, ImageSize -> Tiny, ControlPlacement -> 34}, {{$CellContext`f0Basis$$, "true", "f0 basis"}, { "true", "insured", "insurer"}, Enabled -> Dynamic[$CellContext`tab$$ === "traditional"], ControlPlacement -> 35}, {{$CellContext`xBasis$$, "acc. prob.", "x coord. basis"}, { "acc. prob.", "acc. prob. \[Times] coverage"}, Enabled -> Dynamic[$CellContext`tab$$ === "traditional"], ControlPlacement -> 36}, {{$CellContext`\[Lambda]Multiply$$, False, "multiply x-coordinate of points by \[Lambda]"}, {False, True}, Enabled -> Dynamic[$CellContext`tab$$ === "traditional"], ControlPlacement -> 37}, {{$CellContext`yBasis$$, "risk aversion", "y coord. basis"}, { "risk aversion", "care", "insurance", "responsiveness"}, Enabled -> Dynamic[$CellContext`tab$$ === "traditional"], ControlPlacement -> 38}, {{$CellContext`showInsureds$$, True, "show insureds as points"}, {True, False}, ControlPlacement -> 39}, {{$CellContext`showPremiumLines$$, True, "show premiums"}, { True, False}, ControlPlacement -> 40}, {{$CellContext`showConditions$$, False, "show conditions"}, { True, False}, Enabled -> Dynamic[$CellContext`yBasis$$ === "care"], ControlPlacement -> 41}, {{$CellContext`showCoverageRamps$$, False, "show coverage ramp", Enabled -> False}, {True, False}, ControlPlacement -> 42}, {{$CellContext`pointSizeBasis$$, "insurance", "point size basis"}, { "insurance", "coverage", "insurance\[Times]coverage"}, Enabled -> Dynamic[$CellContext`tab$$ === "traditional"], ControlPlacement -> 43}, Pane[ OpenerView[{"visualization", Column[{ Manipulate`Place[15], Manipulate`Place[16], PaneSelector[{"cluster statistics" -> Column[{ Manipulate`Place[17], Manipulate`Place[18], Manipulate`Place[19]}], "histogram" -> Column[{ Manipulate`Place[20], Manipulate`Place[21]}], "grid" -> Dynamic[$CellContext`pickColumns = Range[13]; Pane[ CheckboxBar[ Dynamic[$CellContext`pickColumns], Thread[ Range[13] -> { "id", "true risk", "insured perceived risk", "insurer perceived risk", "loss", "risk aversion", "responsiveness", "insurance", "care", "\[ScriptS]", "acc. prob.", "cov.", "\[ScriptCapitalE]"}], Enabled -> $CellContext`tab$$ === "grid"], {390, 140}]], "raw" -> Column[{ Manipulate`Place[22], Manipulate`Place[23]}], "trajectory" -> Column[{ Manipulate`Place[24], Manipulate`Place[25], Manipulate`Place[26], Grid[{{ Manipulate`Place[27], Manipulate`Place[28]}, { Manipulate`Place[29], Manipulate`Place[30]}}]}], "traditional" -> Column[{ Grid[{{ Manipulate`Place[31], Manipulate`Place[32]}, { Manipulate`Place[33], Manipulate`Place[34]}}], Manipulate`Place[35], Manipulate`Place[36], Manipulate`Place[37], Manipulate`Place[38], Row[{ Manipulate`Place[39], Manipulate`Place[40]}], Row[{ Manipulate`Place[41], Spacer[18], Manipulate`Place[42]}], Manipulate`Place[43]}]}, Dynamic[$CellContext`tab$$]]}]}], 368]}, "Options" :> { LabelStyle -> {FontFamily -> "Swiss", FontSize -> 11}, ControlPlacement -> Left}, "DefaultOptions" :> {}], ImageSizeCache->{831., {256., 264.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{ 3.5277698634514637`*^9, 3.527769899714265*^9, 3.527770252028241*^9, 3.527770941362687*^9, {3.527771175509396*^9, 3.5277712006988792`*^9}, { 3.527771466024249*^9, 3.527771486081312*^9}, 3.527773555143943*^9, 3.5277765586483307`*^9, 3.527777603406797*^9, 3.527777677087543*^9, 3.5277780446435833`*^9, 3.527778626170471*^9, 3.5277787620734377`*^9, 3.5277793855253153`*^9, 3.527779701009939*^9, 3.527779737391136*^9, 3.527935767757279*^9, 3.527936144462985*^9, 3.527936227927464*^9, 3.527936609158896*^9, 3.528123491035603*^9, 3.528125462229495*^9}] }, Open ]] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell[TextData[{ "The ", StyleBox["Mathematica", FontSlant->"Italic"], " behind the Insurance System Manipulate" }], "Section", CellChangeTimes->{{3.527345005006229*^9, 3.5273450145229273`*^9}}], Cell["\<\ One final function that creates the contract trajectories and presents \ multiple visualization of the system' s evolution\ \>", "ItemNumbered", CellChangeTimes->{{3.5277781908338547`*^9, 3.52777819480121*^9}, { 3.527778230127005*^9, 3.527778276822789*^9}}], Cell["\<\ insuranceSystem[clusterStatisticsPalette_, f0Basis_, firstPointDirectives_, \ fpiters_, histogramLayout_, histogramPalette_, imax_, imin_, loadBasis_, m1_, \ m2_, pointSizeBasis_, q0Control_, quantileAdjustmentFactor_, safetyQuantile_, \ showConditions_, showCoverageRamps_, showInsureds_, showPremiumLines_, tab_, \ trajectoryColorPalette_, trajectoryShow_, v1_, v2_, xBasis_, xhighControl_, \ xlowControl_, yBasis_, yhighControl_, ylowControl_, \[CapitalEta]_, \ \[Lambda]0_, \[Lambda]cc_, \[Lambda]direct_, \[Lambda]Multiply_, \[Lambda]\ \[Rho]_, \[CapitalPi]0_, \[Rho]_] := Module[{\[Lambda]$ = Switch[loadBasis, \"direct\", \[Lambda]direct, \"parametric\", \[Lambda]0 + \[Lambda]cc (m1 m2 - 1) + \[Lambda]\[Rho] \ \[Rho]], q0$ = Round[Rescale[q0Control, {0, 1}, {0.01`, 1}], 0.01`], is$ = \ {365, 408}, ps$ = {380, 460}, cfct$, ct$, stage2$, final$, \[CapitalChi]$, \ pts$, linePrims$}, cfct$ = clusteredForContractTrajectory[\[ScriptCapitalP], \ {m1, m2}, \[CapitalPi]0, q0$, \[Rho], \[Lambda]$, {imin, imax}, ixmStandardC, \ truePerceptionMatrixC, insuredPerceptionMatrixC, make\[CapitalChi], \ quantileAdjustmentFactor]; ct$ = Map[contractTrajectory[Sequence @@ #1, \ fpiters] &, cfct$, {2}]; stage2$ = MapThread[ReplacePart[#1, 2 -> #2] &, \ {cfct$, ct$}, 2]; final$ = Map[Function[cluster$, Insert[cluster$, \ (optimalSolutionC[#1[[{1, 4, 5, 6}]], Take[Last[cluster$[[2]]], 2], \[Rho], \ {imin, imax}] &) /@ First[cluster$], 3]], stage2$, {2}]; Pane[Switch[tab, \"traditional\", Module[{xlow$ = xlowControl, xhigh$ = xhighControl, \ ybounds$ = Switch[yBasis, \"risk aversion\", {0, 1}, \"care\", {0, 2}, \"insurance\", {0, 1}, \"responsiveness\", {0, 50}], ylow$, yhigh$}, ylow$ = \ Rescale[ylowControl, {0, 1}, ybounds$]; yhigh$ = Rescale[yhighControl, {0, \ 1}, ybounds$]; traditionalView[final$, 61, {m1, m2}, f0Basis, xBasis, \ \[Lambda]Multiply, yBasis, pointSizeBasis, {0.005`, 0.02`}, showPremiumLines, \ showInsureds, showConditions, showCoverageRamps, yBasis, {xlow$, xhigh$}, \ {ylow$, yhigh$}]], \"cluster statistics\", clusterStatisticsTabView[final$, \ clusterStatisticsPalette, {v1, v2}], \"histogram\", spectralHistogramVisualization[final$, \[CapitalEta], \ ChartLayout -> histogramLayout, ChartStyle -> Flatten[{myRed, mySeaFoam, \ Table[ColorData[histogramPalette][i], {i, 1, 10}], \ Table[ColorData[Mod[histogramPalette + 1, 62, 1]][i], {i, 1, 10}]}]], \"grid\", gridView[final$, 61, pickColumns], \"trajectory\", trajectoryView[final$, trajectoryShow, \ firstPointDirectives, trajectoryColorPalette, PlotRange -> Module[{xlow$ = \ xlowControl, xhigh$ = xhighControl, ybounds$ = {-1, 2}, ylow$, yhigh$}, ylow$ \ = Rescale[ylowControl, {0, 1}, ybounds$]; yhigh$ = Rescale[yhighControl, {0, \ 1}, ybounds$]; {{xlow$, xhigh$}, {ylow$, yhigh$}}], ImageSize -> 300], \"raw\", rawView[final$, {v1, v2}]], ps$, Scrollbars -> {True, True}]]\ \>", "ProgramNumbered", GeneratedCell->False, CellAutoOverwrite->False, CellChangeTimes->{{3.527777714490736*^9, 3.52777795629316*^9}, { 3.5277779999607973`*^9, 3.527778002435453*^9}, 3.527778121440289*^9, 3.5277782074999113`*^9}], Cell["\<\ Extensive use of OpenerGroup, PaneSelector and the Enabled option for context \ sensitive controls\ \>", "ItemNumbered", CellChangeTimes->{{3.527777366616829*^9, 3.527777389248911*^9}, { 3.527777543670014*^9, 3.527777554492359*^9}}], Cell["\<\ OpenerView[{\"regulatory\", Column[{Control@{{\[Rho], 0.1, \"condition radius (\[Rho])\"}, 0.01, 0.3, \ 0.01, Appearance -> \"Labeled\", ImageSize -> Small}, Control@{{loadBasis, \"direct\", \"load calculation method\"}, \ {\"direct\", \"parametric\"}}, PaneSelector[{\"direct\" -> Column[{Control@{{\[Lambda]direct, 0, \ \"direct load\"}, -0.9, 1, 0.01, Appearance -> \"Labeled\", ImageSize -> \ Small}}], \"parametric\" -> Row[{Column[{Control@{{\[Lambda]0, 0, \"baseline \ load\"}, -0.9, 1, 0.01, Appearance -> \"Labeled\", ImageSize -> Small}, Control@{{\[Lambda]cc, 0, \"cluster count coefficient\"}, -0.2, \ 0.2, 0.005, Appearance -> \"Labeled\", ImageSize -> Small}, Control@{{\ \[Lambda]\[Rho], 0, \"\[Rho] coefficient\"}, -0.9, 1, 0.01, Appearance -> \ \"Labeled\", ImageSize -> Small}}], \"\[Lambda]:\", Spacer[6], Dynamic[\ \[Lambda]0 + \[Lambda]cc*(m1*m2 - 1) + \[Lambda]\[Rho]*\[Rho]]}]}, \ Dynamic[loadBasis]], Control@{{imin, 0, \"minimum permitted insurance\"}, 0, 0.9, 0.1, \ Appearance -> \"Labeled\", ImageSize -> Small}, Control@{{imax, 1, \"maximum permitted insurance\"}, 0.1, 1, 0.1, \ Appearance -> \"Labeled\", ImageSize -> Small}}]}]\ \>", "ProgramNumbered", CellChangeTimes->{3.527778401842936*^9}], Cell["\<\ Controls that determine initial premiums, initial condition quantiles, and \ parameters for adjusting quantiles when the system blows up\ \>", "ItemNumbered", CellChangeTimes->{{3.527777416869236*^9, 3.5277774491885242`*^9}}], Cell["\<\ OpenerView[{\"advanced system evolution controls\", Column[{ Control@{{safetyQuantile, 0.5, \"safety quantile\"}, 0.1, 0.9, 0.1, \ Appearance -> \"Labeled\", ImageSize -> Small}, Control@{{\[CapitalPi]0, 0, \"initial premium\"}, 0, 1, 0.01, ImageSize \ -> Small, Appearance -> \"Labeled\"}, Row[{Control@{{q0Control, 0.25, \"quantile\"}, 0, 1, 0.01, ImageSize -> \ Small}, Spacer[10], Dynamic[Round[Rescale[q0Control, {0, 1}, {0.01, 1}], \ 0.01]]}], Control@{{quantileAdjustmentFactor, 0.7, \"quantile adjustment factor\"}, \ 0.01, 0.99, 0.01, Appearance -> \"Labeled\", ImageSize -> Small} }] }]\ \>", "ProgramNumbered", CellChangeTimes->{3.527778337795217*^9}], Cell["\<\ Controls that permit floors (mandatory insurance) and caps (uninsurable loss) \ on insurance\ \>", "ItemNumbered", CellChangeTimes->{{3.527777462994219*^9, 3.52777749079403*^9}}], Cell["\<\ Control@{{imin, 0, \"minimum permitted insurance\"}, 0, 0.9, 0.1, Appearance \ -> \"Labeled\", ImageSize -> Small}, Control@{{imax, 1, \"maximum permitted insurance\"}, 0.1, 1, 0.1, Appearance \ -> \"Labeled\", ImageSize -> Small}\ \>", "ProgramNumbered", CellChangeTimes->{3.527778306406951*^9}], Cell["Choice of directly set or parametrically set load", "ItemNumbered", CellChangeTimes->{{3.527777342067239*^9, 3.527777359549367*^9}}], Cell["\<\ \[Lambda]$ = Switch[loadBasis, \"direct\", \[Lambda]direct, \"parametric\", \[Lambda]0 + \[Lambda]cc (m1 m2 - 1) + \[Lambda]\ \[Rho] \[Rho]] \[Lambda]$ = Switch[loadBasis, \"direct\", \[Lambda]direct, \ \"parametric\", \[Lambda]0 + \[Lambda]cc (m1 m2 - 1) + \[Lambda]\[Rho] \[Rho]]\ \>", "ProgramNumbered", CellChangeTimes->{{3.527778429187297*^9, 3.5277784373240147`*^9}}], Cell["\<\ Use of Pane in the controls section to tightly control layout\ \>", "ItemNumbered", 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