Optimal insurance contract with stochastic background wealth

Abstract

This study presents an optimal insurance contract developed endogenously when insured individuals face two mutually dependent risks, background wealth and insurable loss. If background wealth is conditionally normally distributed given insurable loss, the optimal insurance contract may be proportional coinsurance above a straight deductible for a quadratic, negative exponential, or mean-variance utility function. Additionally, when the insured has a quadratic utility or mean-variance utility, the optimal retained schedule is a function of conditional expected value of background wealth given insurable loss. Moreover, the optimal insurance contracts for quadratic and negative exponential utility functions need not to be mean-variance efficient, even when the conditional normal distribution is assumed. Finally, when a portfolio problem is considered, the calculation about the optimal insurance contract remains almost unchanged.