Optimal Reinsurance And Investment Portfolio Problem In The Presence Of Stochastic Volatility For An Insurer With Default Risk

Since the reform and opening, our country social development by leaps and bounds has made remarkable achievements. Many technological innovation and financial innovation also accelerating the speed of gradually. For example, our country appeared an upsurge of Internet financial after the country put forward the concept of "Internet +" in 2015. And the people who live in a society all faced kinds of risks by more and more big. In order to spread risk or guarantee risk of the unknown, people usually choose to cover in an insurance company, so the insurance company also more and more popular. Insurance company mainly charged people's premium to profit at the time of the emerging to maintain the survival. But now the increasing competition in the insurance industry, insurance company also can through reinsurance and investment and other means to reduce risk, expand the benefits to ensure that the company more competitive. On the one hand insurance company can spread their risk by reinsurance to put more than their compensation ability of the risk on to other insurance companies. On the other hand, they can investment to the risk free markets, such as Banks and bonds. They can also investment to market risk, such as stock. They also can invest in corporate bonds, etc. Before the vast majority of literature, this is a fixed constant in the market rate of return and volatility, but they are all with an external variables of economic factors in this paper.This article is inspired by Badaui(2013), assuming that the insurance company can undertake excess of loss reinsurance, at the same time invest surplus to risk and risk free markets, and then use the standard of maximize the expected utility of value the terminal time, and assume that the utility function is exponential utility function, using stochastic control theory and dynamic programming method, obtained the optimal retention of excess of loss reinsurance and the best strategy of investment in the risk market, and make the evaluation function to get the maximization of insurance company.On the other hand, inspired by Zhu(2015), assuming that insurance companies invest surplus to market risk, risk free and defaults in the corporate bond market, at the same timeto excess of loss reinsurance risk. The utility function is exponential utility function,respectively discusses the corporate bonds in the case of breach of before default and after default. After default, the company's best strategy is not to invest in corporate bonds to conclude the results in chapter 3, but the company before default can be to invest in corporate bonds, using the theory of stochastic control gain best strategy with investment in the risk market and gain best strategy in the default of corporate bonds and the optimal retention of excess of loss reinsurance, and the numerical solution and evaluation function expressions.