The Optimal Investigation-Reinsurance Strategy With Ambiguity Aversion Under Inflaltion Risk

With the development and progress of the times,people’s awareness of insurance purchase continues to increase,and the purchase of insurance products has become a part of people’s daily life.With the continuous expansion of insurance company business,insurance companies have become an important component of financial institutions.In order to maintain the stability of their own operations and achieve profit goals,while avoiding excessive risks caused by the accumulation of insurance business during the insurance process,insurance companies will choose to diversify their risks by purchasing reinsurance from reinsurance companies,and also invest a portion of their funds in the financial market to obtain returns.In the real financial market,when insurance companies invest,inflation and the ambiguity of insurance companies in the financial market have become inevitable influencing factors,which have a significant impact on the reinsurance investment of insurers.Therefore,in order to better fit the investment situation in the real financial market,we considered the optimal reinsurance investment problem for ambiguity aversion insurance companies in the context of inflation.Firstly,this article investigates the optimal reinsurance investment strategy problem of insurance companies in the context of inflation.Consider insurance companies using proportional reinsurance to diversify risks,while investing surplus funds into risk-free and risky assets.Assuming that the risk-free interest rate is expressed as a deterministic interest rate function,and the price of risky assets follows the B-S model.Under inflation,after the risk assets are converted to inflation,with the goal of maximizing the wealth utility at the end of the period,the corresponding HJB equation is established by using Girsanov transformation and dynamic programming principle,and the explicit solution of the optimal reinsurance investment strategy of insurance companies under expected utility is obtained,thus the optimal reinsurance investment strategy of insurance companies under inflation is obtained.Secondly,on the basis of inflation,we consider the optimal reinsurance investment strategy problem for ambiguity aversion insurance companies.In order to further approach reality,we have chosen the CEV model for this part of the risk asset model.Assuming that the ambiguity aversion type can purchase proportional reinsurance and invest in a portfolio consisting of risk-free assets and risky assets at any time,after converting risky assets to inflation,under model uncertainty,using Girsanov transformation and dynamic programming principles,an explicit solution for the optimal reinsurance investment under CARA utility is obtained.Finally,numerical simulation and economic explanation are given.Finally,numerical simulation is done to analyze the influence of relevant parameters on the optimal reinsurance strategy and optimal investment strategy of insurance companies.The results show that the optimal reinsurance strategy is negatively correlated with the earnings coefficient of the insurance company and positively correlated with the safety coefficient of the reinsurance company without considering the ambiguity aversion.The optimal investment strategy of insurance companies is negatively correlated with the inflation coefficient.When ambiguity aversion is considered,insurance companies’ ambiguity aversion to financial markets will reduce the value of their optimal reinsurance strategy and optimal investment strategy,that is,insurance companies tend to invest in risk-free assets to ensure the stability of profits.