Optimal Investment And Reinsurance Strategies In Dangerous And Safe Regions Under Fuzzy Aversion

With the advancement of modern technology and civilization,the financial in-dustry is booming.A prosperous economic market is not only an opportunity but also a challenge for insurers.Therefore,the decision of the management plays a vital role in the long-term development of insurers.In order to improve their solvency,insurers generally increase returns by investing in risky assets,while purchasing rein-surance to share risks.Therefore,scholars have always been focus on the optimal strategies.Most of the current research on optimal strategies uses models construct-ed from historical data.These optimal strategies that ignore the problem of model uncertainty often mislead insurers' decisions and affect their smooth operations,thus ambiguity aversion comes into being.Regarding the research on ambiguity aversion,most of the literatures aim at maximizing expected utility,and only a few literatures study optimal strategies based on minimizing the probability of ruin.Since insurer prefers to maintain the value of surplus at or above a certain positive,this thesis considers the optimal investment-reinsurance strategies in danger-zone and safe-region under ambiguity aversion.This thesis mainly considers the following two aspects.On the one hand,we consider the robust optimal investment reinsurance strategy of the minimizing prob-ability of drawdown for an ambiguity aversion insurer;on the other hand,we con-sider the minimizing expected time to reach a given capital level under ambiguity aversion.When constructing robust optimal problems,a penalty function is used to punish the uncertainty of the model,and the relative entropy is used to represent the difference between the alternative model and the reference model.Through the robust control theory and the H JBI equation,we obtain the minimizing probability of drawdown under ambiguity aversion and the minimizing expected time to reach a given capital level.Ambiguity is embodied in the model uncertainty of the insur-ance market and financial market in this article.Through the numerical analysis,we conclude that insurers should pay more attention to the uncertainty insurance market.In a word,the management of insurers should not rely too much on the fi-nancial market,but should focus on establishing accurate insurance market models.We also conclude the insurer who has completed the accumulation of original capital wants to achieve rapid earnings growth,it must abandon ambiguity aversion.