Optimal Investment And Reinsurance For An Insurer Under Markov-Modulated Financial Market

Investment is one of the main ways for ?nancial instruments to make pro?ts and reinsurance is the main way for insurers to transfer risk loss and reduce the amount of capital needed to provide coverage. Therefore, it is of great importance for insurers to increase ?nancial pro?t and decrease the claim risk by adopting suitable investment and reinsurance strategies, sometimes even seeking for the best ones. Naturally, more and more industry participants and academic scholars pay attention to the research on optimal investment and reinsurance in recent years, and this is also the main topic to be discussed in this thesis. In this thesis, we introduce two models, one is the classical surplus model and the other one is a ?nancial market model, whose coe?cients are modulated by an external Markov process. The ?nancial risky model considered in this paper can cover a wide range of stochastic ?nancial models, such as several important stochastic volatility models. Precisely speaking, we assumes that the ?nancial market is driven by a drifted Brownian motion with coe?cients modulated by an external Markov process, which is speci?ed as the solution to a stochastic di?erential equation.The object of the insurer is to maximize the expected terminal utility. By dynamical programming method, the Hamilton-Jacobi-Bellman(HJB for short) equation satis?ed by value function is derived. When the utility function is exponential function, the closed form expressions for optimal strategies and the value function are derived. Ruin probability for the insurer is also studied when the insurer adopts optimal investment and reinsurance policies. As a result, we ?nd that under optimal control strategies, the asymptotic decay of ruin probability is greatly larger than the ordinary insurer when the initial surplus tends to in?nity.