Actuarial Science Seminar: The Effect of Risk Constraints on Optimal Insurance Contracts

Abstract: This paper studies optimal insurance policies that maximize the decision maker's expected utility under distortion risk constraints. The problem has been studied in Huang (2006) and Bernard and Tian (2010), who concluded that under Value at risk (VaR) constraints on either the insured or the insurer side, the optimal ceded function may contain jumps. This is undesirable because it would lead to ex-ante moral hazard. Therefore, in our study, we require that both the ceded and retained loss functions are non-decreasing and continuous, which eliminates the moral hazard issues. In addition, we generalize the VaR risk constraint to the distortion risk measure. The impact of the different risk constraints on the optimal policy are discussed in detail. The talk is based on joint work with Wenjun Jiang.
* zoom link available upon request