Time-consistent mean-variance reinsurance-investment in a jump-diffusion financial market

This paper study an optimal time-consistent reinsurance-investment strategy selection problem in a financial market with jump-diffusion risky asset, where the insurance risk model is modulated by a compound Poisson process. The aggregate claim process and the price process of risky asset are correlated by a common Poisson process. The objective of the insurer is to choose an optimal time-consistent reinsurance-investment strategy so as to maximize the expected terminal surplus while minimizing the variance of the terminal surplus. Since this problem is time-inconsistent, we attack it by placing the problem within a game theoretic framework and looking for subgame perfect Nash equilibrium strategy. We investigate the problem using the extended Hamilton–Jacobi–Bellman dynamic programming approach. Closed-form solutions for the optimal reinsurance-investment strategy and the corresponding value functions are obtained. Numerical examples and economic significance analysis are also provided to illustrate how the optimal reinsurance-investment strategy changes when some model parameters vary.