Robust Optimal Reinsurance-investment Strategy Of The Insurance Company

With the enhancement of the people's insurance awareness in China,purchasing insurance products has become one of the main ways for people to plan their lives.The business of insurance company has begun to expand and has become an important part of financial institutions.In order to be able to operate stably for a long time and achieve profit goals,insurance company on the one hand will diversify risks by purchasing reinsurance,and on the other hand,the surplus will be invested in the financial market to obtain benefits.Therefore,the optimal reinsurance and investment strategies of insurance company have been attracting attention.In this paper,the stochastic dynamic programming approach is used to study the robust optimal reinsurance and investment strategies under delayed claims and related claims.Finally,numerical examples are given to illustrate our results.In the first part,we considers the robust optimal control problem under the influence of delayed claims.The surplus process of the insurance company is assumed to invest in a risk-free asset and a risky asset.We build a robust optimization system for model uncertainty,and use the stochastic dynamic programming approach to establish the corresponding HJB(Hamilton-Jacobi-Bellman)equation.The robust optimal reinsurance and investment strategies that maximizing the expected utility of the terminal wealth are explicitly derived.Through the numerical analysis,it can be seen more intuitively that considering delay claims can help insurance company better avoid the risk of huge claims,and then realize the smooth operation of insurance company.In the second part,we analyze the robust optimal strategy of insurance company under the influence of related claims.The surplus process of the insurance company is assumed to invest in a risk-free asset,a stock asset and a default bond.We build a robust optimization system for model uncertainty,and use the stochastic dynamic programming approach to establish the corresponding HJB equation.The robust optimal reinsurance and investment strategies that maximizing the expected utility of the terminal wealth are explicitly derived.Through the numerical analysis,it can be easy seen that considering the correlated of claims can help insurance company better avoid the risk of claims,reduce the proportion of reinsurance,and then save operating costs.Through the numerical analysis,it can be seen that considering the correlated claims can help insurance company better avoid the risk of claims,reduce the proportion of reinsurance,and then save operating costs.