Optimal Claims in Automobile Insurance

Itzahk Venezia and Haim Levy

Rodney L. White Center for Financial Research Working Papers from Wharton School Rodney L. White Center for Financial Research

Abstract: In automobile insurance the premium rate which the insured must pay increases whenever he files a claim. Here we present the optimal claims strategy of the insured. It is shown that the insured will file a claim only if the damage exceeds some critical value which depends on his premium rate and on time. We present a method for obtaining the critical values, and investigate some of their properties. We investi-gate the effect of increasing the risk of the damages distribution on the claims policy and on the welfare of the insured (we used Rothschild and Stiglitz’s [1970], and Diamond and Stiglitz’s [1974] definitions of increased risk). Surprisingly, we show that increased risk may improve the welfare of the insured. We also explore the effect of increased current income on the optimal claims policy, and show that such an increase tends to augment the critical values. Further intuitive properties of the optimal claims policy are provided in a numerical example.

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