Stackelberg Insurance And Reinsurance Optimal Differential Games Under Asymmetric Information

Insurance and reinsurance problems have always been an important field of financial mathematics research.This thesis mainly attempts to study the optimal control and game problem between insurance companies and reinsurance companies under asymmetric information.Considering the deficiency of optimal control and game theory,this paper studies the optimal control problem of insurance company and reinsurance company under internal information and Stackelberg game problem of insurance company and reinsurance company under internal information.First,a stochastic control model of insurance market with one reinsurance company and two insurance companies is constructed.In order to ensure consistency with the actual situation of the insurance market,we assume that reinsurance companies have more future information.At the same time,two insurance companies have a certain degree of correlation,and the it studies the optimal control problem of one main and two subordinate insurance companies.This paper then makes use of stochastic control related theories and uses Bellman dynamic programming principles to obtain HJB equations of corresponding problems.Referring to the dimension reduction method of the equation and the related solution of ordinary differential equation,this paper obtains the analytical expression of the optimal control of reinsurance company and two insurance companies.Further,the "supply and demand balance" of the optimal reinsurance ratio between insurance companies and reinsurance companies is utilized to establish the market connection between reinsurance companies and insurance companies,and the "equilibrium reinsurance premium" of reinsurance companies about the two insurance companies is solved.At the same time,the influence of correlation coefficient on optimal control is analyzed.Next,we extend the control problem to the game problem and establish a Stackelberg game model between insurance companies and reinsurance companies under internal information.This model can solve the problem of laxity in the "supply and demand balance" method.At the same time,for the problem of describing the information asymmetry between insurance companies and reinsurance companies with observable domain flow sizes,which is difficult to solve for the optimal game of reinsurance companies,we use the method of measure transformation to define different measures under the same domain flow,describe the information asymmetry between insurance companies and reinsurance companies,and further solve the equation solution of the optimal game between insurance companies and reinsurance companies.Unlike the general control problem and the non-zero-sum game problem in which equal market players participate.which needs to solve linear PDE,there is a master-slave relationship between reinsurance companies and insurance companies in Stackelberg game,which needs to solve a nonlinear PDE.The expression for the optimal reinsurance premium includes a Riccati equation,which in general cannot obtain an analytical solution.Therefore,we use the difference method to obtain the numerical solution of this equation.When numerically solving the Stackelberg model,unlike other articles that consider the random part of information drift and time as two completely independent variables when studying internal information,this article believes that the random part of information drift has a distribution dependence on time,and studies the distribution of the random part of information drift at the same time.The results obtained from numerical analysis indicate that reinsurance companies with future information can take the initiative in a trading market full of randomness.This inspires market participants in the insurance and reinsurance market to improve their operational level,strengthen industry research,have a clear understanding of future market prospects,and make more favorable decisions in market activities.