The Research Of CCPI In The Jump-diffusion Model Based On Regime Switching Model

With the rapid development of market economy, the term structure of interest rates are mostly non-linear, non-Gauss, makes the traditional statistical model can’t solve this problem.The state space model is a very important kind of time series model, it can handle nonlinear, non structural model of Gauss. There are many applications in statistics、econometrics and advanced signal processing. In financial markets, because of some uncontrollable unexpected factors and human factors of interference may make in the research on market risk and volatility. The results will change as a result, considering Markov regime switching can solve these sudden factors of influence in the simulation of the financial market. In the stock market, investors of the portfolio is very cautious, so to find a can get the maximum profit, the portfolio strategy can be guaranteed is particularly important. So study the CPPI strategy under the Markov regime switching portfolio strategy is of great theoretical significance and practical significance.It is out of this consideration, this paper first introduces the Markov regime switching, state space model, and Lévy process, jump diffusion model. Then on the basis of these models, first we research CPPI under a regime switching Lévy process, and some important conclusions are obtained. Then we under the special models: the jump diffusion model and the generalized Black-Scholes model to study the CPPI portfolio, and we obtain the specific CPPI portfolio and their expectation and variance.