Interplay of Prevention Efforts and Insurance Demand with Distortion Risk Measures

Abstract

In economic analysis, rational agents typically take actions to lower their risk exposure. These actions include purchasing market insurance and simultaneously engaging in prevention efforts to reduce the size of potential claims (self-insurance) or lower the probability of claims occurring (self-protection). This paper examines the interplay between prevention efforts and market insurance demand within the framework of distortion risk measures. Prevention effort is modeled by the changing pattern of loss distributions, represented by a family of stochastically ordered probability measures. We explicitly characterize the optimal combination of prevention effort and insurance demand under self-insurance and self-protection models when buyers adopt Value-at-Risk (VaR) and convex distortion risk measures. Additionally, we provide comparative static analyses to illustrate the main findings under various settings of premium loading, risk aversion, and loss distribution. Our results indicate that, with an increase in safety loading, the substitution effect between market insurance and self-insurance aligns with most of the existing literature. However, the substitution effect also exists between market insurance and self-protection, differing from the complementary findings in studies such as Ehrlich & Becker (1972) and Bensalem et al. (2020).

Keywords: Prevention efforts, Insurance demand, Self-insurance, Self-protection, Distortion risk measures