Research On The Optimal Investment Reinsurance Problem Under State-dependent Risk Aversion

In the field of actuarial insurance,there have been many research results on the mean-variance criterion,but most of them consider constant risk aversion.In fact,state-dependent risk aversion is more consistent with the reality.This the-sis focuses on mean-variance criterion with state-dependent risk aversion.Because mean-variance criterion causes the problem to be time-inconsistent,we investigate the optimal strategy in the sense of equilibrium within the game theoretic perspective.Firstly,we consider the optimal investment and reinsurance problem under the risk model with Poisson jump.In order to reduce risk and improve the compensation ability,the insurer purchases excess-of-loss reinsurance and invests in the financial market.The financial market consists of one risk-free asset and one risky asset,in which the price of the risky asset is described by geometric Brownian motion.By establishing an extended Hamilton-Jacobi-Bellman(HJB)equation system,the optimal strategy for the problem is obtained.From the result,the optimal investment and reinsurance strategy with state-dependent risk aversion is related to the current wealth level,which is more realistic than the result with constant risk aversion.In addition,the influence of parameters on the optimal investment strategy is Considered through some numerical examples,and we give the economic explanation combined with the reality.Secondly,we consider the robust optimal investment and reinsurance problem under the diffusion model with ambiguity.Assuming that the insurer is ambiguity-averse.The insurer purchases proportional reinsurance and invests in financial products,and the market is the same as the above problem.By establishing an extended Hamilton-Jacobi-Bellman-Isaacs(HJBI)equation system,the robust optimal investment and reinsurance strategy is obtained.In addition,numerical results analyze the influence of risk aversion coefficient,ambiguity-averse parameter,and the price volatility of risky assets.