Optimal Reinsurance and Investment Strategy with Delay in Heston’s SV Model

Abstract

In this paper, we consider an optimal investment and proportional reinsurance problem with delay, in which the insurer’s surplus process is described by a jump-diffusion model. The insurer can buy proportional reinsurance to transfer part of the insurance claims risk. In addition to reinsurance, she also can invests her surplus in a financial market, which is consisted of a risk-free asset and a risky asset described by Heston’s stochastic volatility (SV) model. Considering the performance-related capital flow, the insurer’s wealth process is modeled by a stochastic differential delay equation. The insurer’s target is to find the optimal investment and proportional reinsurance strategy to maximize the expected exponential utility of combined terminal wealth. We explicitly derive the optimal strategy and the value function. Finally, we provide some numerical examples to illustrate our results.