The Optimal Investment Reinsurance Strategy Of The Two Insurance Companies Under The Nonlinear Risk Process

With the improvement of economic level,the people’s awareness of risk prevention has gradually strengthened,buying insurance is people’s first choice to prevent risks,and buying insurance has gradually become one of the important ways for national financial management.With the increase in insurance demand,the business of insurance companies has also expanded,insurance products have become more abundant,and the number of insurance companies in the market has also increased significantly.In the insurance market,insurers generally enhance their competitiveness by reinsurance to transfer risk and invest idle funds in financial markets to increase returns.Therefore,if the insurance company is not well managed,bankruptcy not only affects people’s livelihood but also affects the stability of the financial market,and the operating conditions of insurance companies involve the interests of multiple parties,so it is of practical significance to study the game optimal risk investment reinsurance strategy of the two insurance companies.Reinsurance and venture capital stochastic differential strategies have been extensively studied in recent years,and a large amount of literature has mainly focused on linear risk processes,but using linear risk processes to describe the relationship between reinsurance risk and return may violate the fact that excessive risk exposure may not lead to high rates of return.Therefore,on the basis of considering the secondary nonlinear risk model of proportional reinsurance of internal competition factors in the insurance market,this paper uses the dynamic programming principle to establish the HJB equation and solve the HJB equation,and studies the optimal solutions of reinsurance and venture capital of the two insurance companies under the two conditions of fuzzy neutrality and fuzzy aversion.Then,by dividing the time interval,the Nash equilibrium display solution of the game between the two insurance companies under different time intervals is obtained,and finally the influence of important parameters on the Nash equilibrium solution is explored through sensitivity analysis.This thesis mainly includes the following four parts:In the first part,assuming that the goal of each insurance company is to maximize the exponential utility of the difference between its terminal surplus and that of its competitors at a fixed terminal moment,the authors study the optimal solution of the venture capital and reinsurance strategies of the two insurance companies under the condition of fuzzy aversion neutrality by constructing the HJB equation to solve the equation.In the second part,based on the first part,the author considers the ambiguous aversion of insurance companies,and studies the robust optimal strategies of venture capital and reinsurance of the two insurance companies by constructing the HJB equation.In the third part,the author compares the optimal solution of the risk investment and reproportional insurance strategies of the two insurance companies under fuzzy neutral and fuzzy disgust conditions,finds that the fuzzy disgust degenerates to the fuzzy neutral situation when the fuzzy aversion coefficient is close to infinity,and discusses the Nash equilibrium display solution of the two insurance companies in different time intervals by dividing the time interval.Finally,The author uses Python for sensitivity analysis to explore the influence of important parameters on the Nash equilibrium solution,find that the greater the internal competition factors in the insurance market,the greater the ambiguous disgust coefficient,the more conservative the reinsurance strategy of insurance companies.Insurers are more concerned about wealth differences with competitors,will have more aggressive insurance strategies.