Time-inconsistent Optimal Insurance Investment Decision-making Under The Market Conditions Of No-short Selling

The overwhelming majority of scholars have adopted the "global invariant strategy" to study the optimal investment strategy of insurance companies.That is,the optimal investment strategy formulated by insurance companies after considering the possible situations in the investment process is the only "optimal" strategy adopted by insurance companies in the whole investment process.This method has a certain guiding effect on the optimal investment of insurance companies in the past when the kinds of financial market products are few and the fluctuation is small.However,with the continuous enrichment of the global financial market system and the continuous promotion of marketization,this method is increasingly unable to meet the needs of real investment.Therefore,inspired by the concept of "time inconsistency" in the money market,more and more scholars begin to extend the concept of "time inconsistency" to optimal investment research.Since the concept of "time inconsistency" was proposed by foreign scholars,and in the field of optimal investment,foreign scholars have more abundant theoretical research on "time inconsistency" optimal investment than domestic scholars.Therefore,it is necessary to "sinicize" the existing research abroad and study the optimal investment decision with time inconsistency under the condition that short-selling is not allowed.In this paper,we study the time-inconsistent investment decision-making of insurance companies under the condition that short-selling is not allowed.With the mean-variance criterion as the selection criterion,the square term of expectation in the objective function is obtained,which makes the Bellman criterion no longer applicable.Therefore,the optimal investment decision-making problem studied in this paper has become a problem of time inconsistency.Time inconsistency,also known as dynamic inconsistency,means that the optimal decision in the previous period is not necessarily optimal in the next period.Under the condition of time inconsistency,the traditional optimization criterion is no longer applicable.By using the improved HJB equation and two auxiliary lemmas,this paper obtains the analytical solutions of the optimal static investment strategy,the optimal dynamic investment strategy,the optimal dynamic reinsurance-investment strategy and their respective value functions under the two different situations of investing only in one risky asset and investing in multiple risky assets,respectively,and gives their respective effective frontiers.It isalso found that the separation theorem of the two funds holds in both cases.Finally,using MATLAB software to simulate and analyze the impact of risk-free interest rate changes on the optimal investment strategy under the conditions of short selling and no short selling.Emphasis is laid on the analysis of the impact of market conditions that do not allow short selling on the optimal(reinsurance)investment strategy of insurance companies.