Optimal Investment Strategies Based On Classical And Dual Models Of Fuzzy Aversion

In risk theory,classical models and dual models have been studied for many years.The classical model is generally used to describe the earnings process of insurance companies,while the dual model is suitable for companies with continuous expenses and random returns,such as pharmaceutical or petroleum companies.Reinsurance and investment issues are integral to both models.When a claim occurs,the insurance company cannot afford all the claim amount,so it chooses to transfer part of its risk to the reinsurance company,which can reduce the insurance company's risk.The investment can improve the company's competitiveness,enhance the company's solvency to improve efficiency and operational stability.This paper mainly studies the optimal investment and reinsurance strategies of classical and dual models under ambiguity aversion,and the details are as follows:The first chapter introduces the development of classical model and dual model,and then introduces the current state of research on reinsurance,investment,and ambiguity.The second chapter studies the optimal investment and excess-loss reinsurance strategies when insurance companies have ambiguity aversion to financial market,and there is a correlation between insurance companies and the financial market.Under the goal of maximizing the terminal wealth of insurance companies,the optimal investment and reinsurance strategies and the expression of value function are obtained by using stochastic control methods with exponential utility function.Finally,numerical examples are given to analyze the influence of some parameters on the optimal investment and reinsurance strategies.The third chapter studies the optimal investment strategy under the dual model with perturbations based on ambiguity aversion.The perturbation is added to the dual model,where the perturbation represents the slight change of the current assets.Consider investing in a risk-free asset and a stock,under the exponential utility function,construct the corresponding Hamilton-JacobiBellman(HJB)equation,and finally obtain the optimal investment strategy and the expression of the value function.The fourth chapter studies the optimal investment strategy of the dual model under ambiguity aversion and default risk.There are three kinds of assets in the financial market:a risk-free asset,a stock and a defaultable bond,and the company is related to the financial market.The company invests in these three kinds of assets to maximize the utility function,pre-default case and post-default case,respectively,the HJB equation corresponding to the function,the expression of value function and the optimal investment strategy are obtained,and the numerical examples show that the parameters will affect the investment strategy.