Mean-Variance Investment and Per-Loss Reinsurance Strategies in Contagion Financial Markets

This paper investigates the optimal investment and reinsurance problem for insurers in a financial market with contagion risk. The prices of risky assets are assumed to follow a jump–diffusion model, where the jump component is driven by a multidimensional dynamic contagion process with diffusion (DCPD). This process simultaneously captures jumps triggered by endogenous and exogenous excitations, effectively characterizing the dynamic contagion effects arising from the joint influence of multiple factors in financial markets. The insurer aims to maximize a mean-variance (MV) utility function by purchasing per-loss reinsurance and investing the surplus in the contagion financial market. By solving the extended Hamilton–Jacobi–Bellman (HJB) equations, we derive the time-consistent equilibrium investment and reinsurance strategies, as well as explicit expressions for the equilibrium value function. These results are characterized by two nonlocal partial differential equations (PDEs), whose probabilistic solutions are obtained through the Feynman–Kac formula. Finally, numerical experiments illustrate how equilibrium strategies respond to changes in contagion intensity and confirm the effectiveness of the proposed model.