Several Types Of Optimal Dividend, Investment And Reinsurance Problems For Insurance Companies Under Fuzzy Aversio

In recent years,the insurance market of our country has developed rapidly.In order to realize the benign development in this environment,the insurer must choose the objective function and the optimal strategy according with the objective function reasonably.Therefore,how to select the optimal dividend,optimal investment and optimal reinsurance strategy for insurer has also attracted the attention of many scholars.The insurer usually establishes a reference model and chooses the optimal strategy by calculating the reference model in order to find the optimal strategy which according to the objective function of the insurer.The reference model is usually established by the data obtained by insurer through various business channels and there is a certain deviation from the actual situation.It is necessary to consider the parameters of ambiguity aversion in order to avoid the loss caused by the deviation of the model.Therefore,on the basis of the classical risk model,this paper considers the factors such as boundary dividend,correlated claims and delay.This paper studies the optimal dividend,investment and reinsurance strategies of ambiguity aversion insurer when the models of dividend,financial market and insurance market are ambiguity.By establishing the Hamilton-Jacobi-Bellman equation for different models,the optimal dividend,investment and reinsurance strategies and the value functions of insurer under the corresponding models are obtained.Finally,different numerical examples are given to illustrate the influence of different model parameters on optimal dividend,investment and reinsurance strategies and their practical significance.In this paper,the optimal stochastic control problem of ambiguity aversion insurer is discussed when the model is ambiguity.The first chapter introduces the domestic and foreign research status and research background,and gives the relevant research literature and results.The second chapter studies the optimal dividend strategy with ambiguity aversion under the exponential premium principle.Under the objective of maximizing the expectation of the cumulative dividend,the optimal dividend strategy under this model is obtained by considering the ambiguity of the insurance market and the premium is subject to the exponential premium principle.Finally,a numerical example is given to describe the influence of risk aversion coefficient on optimal dividend strategy.The third chapter studies the optimal investment and reinsurance with correlated claims under ambiguity aversion.In order to minimize the probability of ruin,the situation that the insurer will charge the premium according to the historical claims of the policyholder and the ambiguity model of the insurance market and the financial market has been considered.The optimal investment,reinsurance strategy and the value function are obtained.Finally,the numerical examples are given to describe the influence of the parameters of correlated claims on the optimal investment and reinsurance strategy.The fourth chapter studies the optimal investment and reinsurance problem with delay under ambiguity aversion.Under the objective of maximizing the expectation of exponential utility function,this paper considers that the insurance market and the financial market both have ambiguity and delay,the optimal investment strategy,reinsurance strategy and the value function of the insurer are obtained.Finally,the numerical examples are given to describe the effect of the delay and the ambiguity aversion coefficient on the optimal investment and reinsurance strategy.