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Using Genetic Programming to Improve Liability Insurance

Seth J. Chandler
Organization: Unversity of Houston Law Center

2006 Wolfram Technology Conference
Conference location

Champaign IL

The typical liability insurance contract describes a set of lawsuits for which it wishes to provide protection to the insured and applies a formula to determine the insurer’s payment obligations pursuant to that contract. That formula tends to be rather simple and is generally a function of the judgment that actually materializes against the insured and, primarily in American jurisdictions, on the nature of any offers made to settle the lawsuit. Typically that function is a piecewise continuous linear function of the judgment amount capped by the “policy limit” if the insurer has satisfied its “duty to settle” but is a (continuous) uncapped linear function of the judgment if the insurer is deemed to have breached its duty to settle. Although the function to be applied may vary depending on how the lawsuit is characterized verbally, such as whether it constitutes “advertising injury” or not, the functions do not take into account any statistical characteristics of the ex ante distribution of damages expected in the lawsuit that materializes (“lawsuit statistics”). Moreover, earlier attempts by insurers to use piecewise discontinuous functions are now prohibited in most American jurisdictions. This paper uses Mathematica and the DataModeler package of Evolved Analytics to examine the effects of different forms of liability insurance on the effective cost of accidents facing insureds. It adapts the symbolic regression functionality in the DataModeler package to perform general-purpose genetic programming, which is useful in exploring how payment functions based on lawsuit statistics may prove superior to more traditional payment functions. It also shows how use of dynamic interactivity functions in Mathematica 6 (such as Manipulate) may be used in conjunction with numerical optimization routines to explore the behavior of complex multivariable functions such as those generated in this field. The paper concludes by showing that the insured could lower the cost of accidents it faced by shifting from the traditional statistics-invariant bundled liability insurance contract to several alternative liability insurance contracts. The cost of accidents could be reduced by a currently prohibited piecewise discontinuous linear function in which the obligation of the insurer becomes zero (or even negative) for judgments exceeding a certain threshold amount. The cost of accidents could be reduced by a liability insurance policy that applies different piecewise continuous linear functions depending on lawsuit statistics. Third, the cost of accidents could be reduced by a more complex duty to settle than the law currently imposes. While there are a number of factors that need to be considered—particularly the effect on victim compensation—in assessing any reforms in this field, the substantial savings this article shows to exist in this trillion dollar global industry suggests courts and legislators should reassess their apparent hostility to some of these alternative liability insurance contracts and consider use of a more flexible and sophisticated duty to settle.