Optimal time-consistent reinsurance-investment strategy with delay for an insurer under a defaultable market

Abstract

In this paper, we consider a reinsurance-investment problem with delay for an insurer under the mean-variance criterion in a defaultable market. The financial market consists of a risk-free bond, a stock and a defaultable bond. The insurer's surplus process is described by a jump-diffusion risk model and the price process of the stock is assumed to follow a constant elasticity of variance (CEV) model. In particular, we take the delay of feedback time for strategy into account. Applying stochastic control approach, we derive the time-consistent reinsurance-investment strategy in post-default case and pre-default case explicitly via a game theoretic framework, respectively. Finally, numerical examples and sensitivity analyses are provided to show the impact of financial parameters on the optimal strategies.