相依风险模型下时间一致的最优再保险-投资策略OA

The problem of the time-consistent optimal reinsurance-investment strategy with dependent claims in the Poisson-Geometric risk model was studied.In the model,it is assumed that the insurance company purchases two types of proportional reinsurance,the reinsurance premium is calculated based on the expected-variance principle,and the price of risky investments fluctuates with market inflation.Under the mean-variance criterion,the corresponding Hamilton-Jacobi-Bellman(HJB)equation was established by using the stochastic control theory and dynamic programming,and the analytical solutions to the time-consistent optimal reinsurance-investment strategy and the value function were derived.Finally,with the help of numerical experiments and combined with its economic significance,the impact of the main parameters of the model on the optimal reinsurance-investment strategy was discussed.The results show that the optimal reinsurance strategy decreases with the increase in the expected number of claims and the degree of deviation in the number of claims;in the two types of claim settlement businesses with dependence,the reinsurance strategies adopt opposite strategies as the number of claims and the degree of deviation in the number of claims increase;the optimal investment strategy decreases with the increase in the inflation rate,the return rate of risk-free assets,and the volatility of risky assets.