Alpha-robust investment-reinsurance strategy for a mean-variance insurer under a defaultable market

TL;DR

This paper develops a robust investment-reinsurance strategy for a mean-variance insurer in a defaultable market, deriving explicit solutions and analyzing parameter impacts through numerical examples.

Contribution

It introduces a novel $ ext{ extalpha}$-maxmin mean-variance framework for optimal reinsurance and investment in defaultable markets, with explicit strategies derived via extended HJB equations.

Findings

Explicit closed-form solutions for optimal strategies.

Parameter sensitivity analysis highlights key influences.

Robust strategies outperform non-robust ones under model uncertainty.

Abstract

In this paper, we consider the robust optimal reinsurance investment problem of the insurer under the $\alpha$-maxmin mean-variance criterion in the defaultable market. The financial market consists of risk-free bonds, a stock and a defaultable bond. The insurer's surplus process is described by a L\'{e}vy insurance model. From the perspective of game theory, the extended Hamilton-Jacobi-Bellman equations are established for the post-default and pre-default conditions respectively. In both cases, the closed-form expressions and corresponding value functions of the robust optimal investment reinsurance strategies are derived. Finally, numerical examples and sensitivity analysis are used to illustrate the influence of parameters on the optimal strategies.