Alpha-maxmin mean-variance reinsurance-investment strategy under negative risk dependence between two markets

Abstract

This paper investigates the optimal reinsurance-investment problem in the context of negative dependence between the insurance and financial markets, stemming from the general risk dependence between the jump–diffusion process of risky asset prices and aggregate claims process. Under the $\alpha$-maxmin mean–variance (MV) criterion, the insurer is allowed to purchase per-loss reinsurance and invest in a financial market, with the generalized mean–variance premium principle employed to calculate the reinsurance premium. By solving the corresponding Extended Hamilton–Jacobi–Bellman (EHJB) equation, we derive the $\alpha$-robust equilibrium reinsurance-investment strategy and then discuss the form of the optimal reinsurance strategy. Our findings indicate that, under the assumption of negative dependence, investing can serve as a more effective risk-hedging tool for claims risk, prompting the insurer to favor investing in risky asset while retaining a greater proportion of claims compared to scenarios without such dependence. Furthermore, assuming the presence of negative dependence, the variance premium principle indicates that a combined form of proportional and excess-of-loss reinsurance is optimal, rather than solely proportional reinsurance with the majority of papers recognizing. Finally, a sensitivity analysis is performed with numerical examples, and the impact of various parameters on the results is analyzed.