The Games Between Insurer And Reinsurer Based On The Heston Model Under Inflation

With the rapid development of the insurance industry and the complex changes in the market environment,the risk of insurers facing catastrophe claims is increasing.Insurers usually consider how their own capital can increase in value through investment portfolio and maximize their terminal wealth.They also consider how to transfer the claim risk through reinsurance to minimize the probability of insolvency of insurers.Therefore,the study of reinsurance game is also the focus of managers’ management.Firstly,funds are considered to be invested in three assets: risk-free assets,equities,and zero-coupon bonds.We study the reinsurance investment strategies of insurers and reinsurers based on the Heston model in an inflationary scenario.It is assumed that the price process of risky assets follows the Heston model;the optimal investment strategy is obtained based on the utility maximization of terminal wealth using the dynamic programming principle.The sensitivity analysis of relevant parameters on the reinsurance strategy is obtained by MATLAB software.The research results show that the optimal reinsurance strategy depends on the insurance market parameters;the proportion of investment in financial assets depends on the financial market parameters.Secondly,we consider the fuzzy aversion scenario and study the reinsurance investment of insurers and reinsurers in the stochastic inflation scenario.Suppose there are risk-free assets,risky assets and zero-coupon bonds in the financial market.It is assumed that the interest rate follows the affine interest rate model and the risky asset prices follow Heston’s SV model.The stochastic inflation is inscribed with a formula related to stochastic fluctuations.With the objective of maximizing the utility of terminal wealth,stochastic control theory is used to find the optimal value function and the optimal reinsurance investment strategy.The results show that the volatility of risky assets,stochastic inflation,stochastic interest rates,and model uncertainty all have different degrees of influence on the robust optimal reinsurance-investment strategies of insurers and reinsurers.Finally,we analyze the impact of relevant parameters in the model on the optimal strategy.Finally,the full paper is summarized and an outlook of the problem research is given.