Using Mathematica 6 To Inform Political Debate

The Texas Windstorm Insurance Simulator

Professor Seth J. Chandler

University of Houston Law Center

Why should you spend 20 minutes here given that you don't live in Texas?

Example of what is possible using the Version 6 front end

radio button grids , dynamic objects in the controls, interacting sliders, complex layouts

Exploring the boundaries of Demonstrations

screen real estate limitations, control complexity limitations

Other jurisdictions have political issues too

Guess who is likely going to have to come to Texas' rescue when it makes short sighted choices?

The Texas Windstorm Insurance Association (TWIA)

The Texas Windstorm Insurance Association is a regulated, statutory body that insures residential and business property against windstorm property damages in coastal counties in Texas

Funding is controversial: some critics say it is subsidized, other critics say premiums are too high

Many object to the fact that the models underlying the rate debate tend to be proprietary and not readily subject to cross examination

Want to know more?

My goal

What I can do

Make the models more accessible

Make the consequences of the model more visual

Permit advocates and regulators to examine the likely consequences of suggested legal reform and differing assumptions

Facilitate rational debate among people without evil intent

What I can' t do yet

Develop better meteorological models or civil engineering models

Eliminate greed

coastal homeowners

insurers

proprietary modelers

Entirely rationalize politics

What I Did

Read up on hurricane models

Read the Texas statutes and regulations

Tooltip["the statute itself",]

Imported data in Excel format from Texas Windstorm Insurance Association correlating insurance policies with geographic factors, home value, type of home ownership

Imported 10,000 year storm sets produced by AIR for Texas Windstorm Insurance Association

more on the data

TWIA not eager to have raw data re - released

Created a Model of Windstorms and Their Affects

Creating a Flexible Model of Windstorms and Their Affects

Calculate the probabilities of a windstorm being at the 55 strike county/category combinations

Fit a Poisson Distribution to the data of hurricane frequency per year

Tooltip[Style["how good a fit do we get?","Text"],]

Find "Maximum Likelihood" estimators for the parameters of a  Weibull Distribution (offset) for each of the 55 strike county/category combinations

Tooltip[Style["the Mathematica code behind this","Text"],Style[Defer[mleCountyWeibullParameters[n_,ss_,opts:OptionsPattern[NMaximize]]:=If[MemberQ[Position[countySSTable,_,{2},Heads->False],{n,ss}],With[{data=Last/@countySSTable[[n,ss]]},NMaximize[{Total[Log[Max[10^-20,PDF[WeibullDistribution[a,b],#-c]]]&/@data],And[0.1<a<4.4,3000000<b<9500000000,0.1<c<b Gamma[1+(1/a)]]},{a,b,c},opts]],mleCountyWeibullParameters[n,Max[1,ss-1],opts]]],18]]

Tooltip[Style["finding maximum likelihood estimators using global optimization","Text"],Defer[Monitor[mleCountySSWeibullParametersTable=Outer[(i=#1;j=#2;mleCountyWeibullParameters[##,Method->"SimulatedAnnealing",MaxIterations->250])&,Range[11],Range[5],1,1],{i,j}]]]

And now we can create an essentially infinite number of 10, 000 year storm sets -- and we don' t have to reveal the raw AIR data

And we can also calculate analytically  the expected liability of any layer of insurance for any strike county/category combination, or any strike county, or any cateory or for all of Texas!

Tooltip[Style["it just takes some calculus","Text"],Style[Defer[Integrate[(a (b^(-a)) (E^(-((((x/b)))^a))) (x^(-1+a)))Piecewise[{{0,0<=x<transformeddeductible},{x-transformeddeductible,transformeddeductible≤x≤transformedlimit},{transformedlimit-transformeddeductible,x>transformedlimit}}],{x,0,∞}]]//TraditionalForm,18]]

Tooltip[Style["and Mathematica to help simplify the integral","Text"],Style[TraditionalForm[(Piecewise[{{-transformeddeductible+transformedlimit, transformeddeductible≤0&&transformedlimit≤0}, {-transformeddeductible+(E^(-((((transformedlimit/b)))^a))) transformedlimit+b Gamma[1+(1/a)]-b Gamma[1+(1/a),((((transformedlimit/b)))^a)], transformeddeductible≤0&&transformedlimit>0}, {-(E^(-((((transformeddeductible/b)))^a))) transformeddeductible+(E^(-((((transformedlimit/b)))^a))) transformedlimit+b Gamma[1+(1/a),((((transformeddeductible/b)))^a)]-b Gamma[1+(1/a),((((transformedlimit/b)))^a)], True}}])],14]]

We can also adjust the effects of the windstorm analytically depending on the number of properties insured and the per house/business ceiling on insurance

Putting It All Together

Two Ideas

Creating a model that captures the right variables and that produces useful information

Making that model publicly available

Unveiling my project

Mathematica Implications

Can build sophisticated interfaces using Mathematica

Manipulate and Demonstrations format have limitations

What is often done < what is possible < what one sometimes wants

Complex space-conserving layout using Manipulate is difficult

Need to be very aware of front end timing issues and where to place the Dynamic

Good understanding of Dynamic, Setting extremely useful

Mathematica 6 an Excellent Tool

Reverse engineering models used by experts

Visualization

Interactivity

Rapid prototyping

Publication via Demonstrations and Mathematica Player

Real World Implications Clarified by Model

current system does not adequately protect Texas taxpayers from disaster

consider alternatives to reinsurance such as cat bonds

this is a fixable problem

good climatological data and models are crucial

conflict between proprietary goals of modelers and public debate

want to know more?