A Study Of Optimal Excess Loss Reinsurance And Investment Strategies Under Stochastic Factor Models

Investment and reinsurance are important methods for the insurance company to obtain returns and control risks.In the modern insurance industry,the investment increasingly becoming an important part of the insurance industry,risk models that simultaneously consider reinsurance and investment risks have received much atten-tion in recent years.In addition to investment,people can also consider the concept of reinsurance is incorporated into the model.In fact,the multi-objective optimiza-tion problem that is subject to the dual constraints of investment and reinsurance has become a hot research issue in the field of insurance and actuarial science.On the one hand,the insurer increases their income,expands the company's scale and the ability of insurance to pay by investing in the financial market.On the other hand,in order to spread risks,avoid large claims and excessive concentration of claims leading to company bankruptcy,the insurer will choose to allocate part of the premium to purchase reinsurance.In the choice of the value function,the max-imization of the expected index utility and the minimization of the ruin probability are two important choices in the actuarial research,which have received widespread attention.This thesis mainly studies the expected exponential utility function of the terminal wealth with investment and reinsurance risk models,namely CARA(Constant Absolute Risk Aversion)utility function.In this thesis,we study the problem of excess-of-loss reinsurance and invest-ment for an insurer which wishes maximize the expected exponential utility of the terminal wealth.Firstly,we extend the classic Cramer-Lundberg model,add rein-surance and investment parts,and give the value function of the study.Then,using stochastic control theory,find the Hamilton-Jacobi-Bellman(HJB)equation that the value function satisfies,and solve it obtain the solution of its value function and the corresponding optimal strategy.After that,the verification theorem and the uniqueness of the solution are proved from a theoretical point of view.Finally,the model is numerically analyzed,the sensitivity of some parameters is analyzed.The research on insurance market in the past rarely considered the impact of the environment on insurance and reinsurance.In fact,for insurer,the impact of the environment on their business and decision-making cannot be ignored.We describe the external risk fluctuations as a diffusion process to represent the impact of stochastic factors such as the economy and natural environment on the insurance market,that is,the stochastic factor model,which makes the model closer to reality and has certain practical significance.