The Research Of Optimal Investment And Reinsurance Problem With Delay Under Two Kinds Of Investment Model

Since the expected discounted penalty function is introduced by Gerber (1998),the classical risk model got the attention of more scholars.The classical risk model is compound poisson risk model,but as the economy is increasingly complicated, many scholars on the basis of this made some reasonable pro-motion. Not only the model complicated but also consider reinsurance and investment.This paper introduce a delay of the optimal investment and excess of loss reinsurance on the basis of classical Cramer — Lundbergrisk model.This article mainly study the optimal investment and reinsurance problem with de-lay under two different investment model.we obtain the solution of the optimal strategy and value function by using the stochastic control theory and HJB equation.In this paper, main work is as follows:In Chapter1, we introduce the background and the latest research dynamic of the theory of risk, then present the main work of this article.In Chapter2, we mainly introduce the risk model and the model of the investment associated with this article.In Chapter 3,we discuss the optimal investment and excess of loss reinsur-ance problem with delay under the CEV model.Our objective is to maximize the insurance company terminal wealth and the average expected index utility ,By using the theory of stoehastic control,we obtain the corresponding HJB equation.By means of solving the HJB equation,we get the expression of the value function and optimal strategy.In Chapter 4, on the basis of the Chapter 3,we discuss the optimal in-vestment and excess of loss reinsurance problem with delay under the O - U model.The surplus process is characterized by classical risk model.Insurance companies invest into the risk-free asset and risk asset, The price of risk asset is described by O-U model.At the same time,we allow insurance companies to buy a certain amount of excess of loss reinsurance.Our objective is to maximize the insurance company terminal wealth and the average expected index utility By using the theory of stochastic control,we obtain the corresponding HJB equation.By means of solving the HJB equation,we get the expression of the value function and optimal strategy,and analying the relationship between the related parameters and the optimal strategy.