Research On Optimal Reinsurance-investment Strategy Based On α-maxmin Mean-variance Criterion

In recent years,with the rapid development of insurance market,many scholars have conducted in-depth research on reinsurance-investment problem.Insurer can control risk by investing in financial markets,buying reinsurance,and acquiring new business(acting as reinsurer for other insurer).Reinsurance can effectively spread the risk of huge claims,and the investment of insurance premiums can enable insurer to achieve certain business objectives.As a financial institution whose main business is to undertake risks and disperse risks,insurance company plays an important role in national economic construction and social security.This thesis studies the optimal reinsurance-investment problem of the insurer under the α-maxmin mean-variance criterion.The model allows the insurer to have different degrees of ambiguity aversion.Extreme ambiguity aversion will lead insurer to buy too much reinsurance and thus reduce the profits,because the safety loading of the reinsurer is usually higher than the safety loading of the insurer.So it is reasonable for insurer to be more tolerant of the ambiguity of more experienced businesses.This thesis considers the optimal reinsurance-investment problem of insurer with delay and the optimal reinsurance-investment problem under the a defaultable market respectively under the α-maxmin mean-variance criterion.Based on the dynamic programming principle,the optimization problem and the corresponding HamiltonJacobi-Bellman equation are established respectively,and the optimal reinsurance strategy and the optimal investment strategy are obtained.Finally,the influence of some important parameters on the optimal strategies is illustrated by numerical analysis.The results show that considering the delay information has an important impact on the optimal strategy.The longer the delay,the greater the weight of the final objective function in the early wealth statement,the smaller the overall risk,and the insurer will be willing to take more risks when making the optimal reinsurance and investment strategy.The occurrence of default events has nothing to do with the optimal reinsurance strategy and the optimal investment strategy of stocks,while the risk model of insurance company,the price model of the stock and the degree of ambiguity aversion will affect the investment of the defaultable bond.