Research On The Robust Optimal Reinsurance Investment Strategy For Competing Insurance Companie

With the rapid development of our economy,the business of insurance company began to expand rapidly.In order to achieve long-term stable operation and profit objectives,insurance companies on the one hand,diversify their own risks by purchasing reinsurance and on the other hand,obtain additional income by effectively investing in the financial market.Therefore,the optimal reinsurance and investment problem of insurance company has always been a hot issue.At present,the competition in domestic and foreign insurance markets is becoming increasingly fierce,instability and uncertainty are increasing significantly,and insurance companies are facing greater risks and challenges in capital operation.Therefore,our paper considers the model uncertainty(i.e.robustness)and the non-zero-sum game between insurance companies when studying the optimal reinsurance and investment strategy.In addition,the time consistency of the strategy is also an important and reasonable requirement.Based on the stochastic control theory,dynamic programming principle and other methods,our paper discusses the reinsurance and investment optimization problems under several kinds of complex financial models.The mainly work of this paper are as follow:In Chapter 1,we introduce the research background and significance of our paper,analyze the current situation of research at home and abroad in recent years,make a description of relevant classic papers,and then briefly describe the main content and innovation of our paper.In Chapter 2,we study the robust optimal reinsurance and investment problem with correlated claims under the Ornstein-Uhlenbeck(OU)investment model.Based on the general diffusion model,we consider correlated claims,suppose that the premium is calculated according to the loss-dependent premium principle rather than the expected value principle.Combined with the ambiguity aversion of the decision-makers of insurance company,the explicit solutions of the robust optimal reinsurance and investment strategy and the optimal value function are obtained with the objective of maximizing the expected utility of terminal wealth.Finally,a numerical example is given to illustrate the impact of correlated claims and model robustness on the optimal strategy.In Chapter 3,we consider the non-zero-sum stochastic differential game between two competing insurance companies under the Heston investment model.Assuming that each insurer takes the performance maximization of the relative difference in the terminal wealth of two insurers as the objective,through the game theory and dynamic programming principle,the HamiltonJacobi-Bellman(HJB)equation satisfied by the value function is derived,and the Nash equilibrium reinsurance and investment strategies are obtained respectively when the decision makers are ambiguity-averse and ambiguity-neutral.Finally,a numerical example is given to illustrate the influence of parameters on optimal strategy.In chapter 4,we investigate the robust time-consistent reinsurance and investment problems with two independent classes of insurance business under the mean-variance criterion.It is assumed that the wealth process of insurance company follows the classic Cramer-Lundberg(C-L)model and the approximate diffusion model respectively,and the price process of risky asset follows the Constant Elasticity of Variance(CEV)volatility model.Applying stochastic control theory,we establish the extended HJB equation and derive the closed-form expressions of the robust equilibrium strategy and the corresponding equilibrium value function both in the classical C-L model and its diffusion approximation model.Finally we present numerical examples to illustrate the effects of model parameters and some interesting conclusions are found.