The Risk Model Of The Optimal Investment And Reinsurance About The Disturbance Factor

An insurance company receives the premium but it also will face the risk of paying the claim. Sometimes. ruin will occur when the claim is higher than its surplus. Therefore, how to get the reasonable strategy(for example, the reasonable reinsurance strategy or the reasonable investment strategy)which is optimal in the sense of maximizing(or minimizing)some objective function becomes the hot problem for insurance company. In the past ten years, optimal investment and reinsurance problems bave gained much interest in financial and actuarial literature. The purpose of this paper is to be familiar with optimal investment and the optimal investment theory of the risk model in reinsurance and related problems of risk model in which the risk process for an insurer has a compound Poisson process as the distribution.To be more specific, we consider an insurer invests part of his surplus into the stock and bond market as well as buys reinsurance to reduce the risk for reduce huge losses to their probability. In this paper, based on the classical risk model with the conclusions, and have made the simple introduction after some promotion's investment reinsurance risk model. We will make double generalized Poisson about interest rate and the disturbance factor promote to the two-dimensional renewal risk model, and study the Lundberg inequality that the ruin probability will satisfy. Furthermore, we prove a certain integro-differential equation of the survival probability by use of the It? formula and prove the existence of the solution of the equation. And then we give the Laplace equation of the survival probability to get the numerical solution through the computer when the distribution of the claim size has been given. we also discuss the optimal investment and proportional reinsurance for the two-type-risk insurance. Assuming that the reinsurance premium is calculated according to the expected value principle, it gives the example that the explicit forms of optimal investment and optimal reinsurance rate contract according to HJB equations. We also conclude that the case with investment the expected value of the surplus is always better than the one without investment the expected value of the surplus. Some numerical examples are given, which illustrate the results of this paper.