Study On The Optimal Consumption And Portfolio Of Jump Diffusion Process

There are five sections in this thesis. In the 1st section, we briefly review the development of financial theory, and introduce the research work ahout financial problems, where the price of these financial assets with mixed jump-diffusion process. In 2nd section we have reviewed the main theory of BSDE and BSDE with jumps. In the 3rd section we introduce how to use mathematical model to study financial problems, whose assets running on mixed jump-diffusion process, first we get the famous non-linear Feynman-Kac formula by FBSDE, then let the solution of the BSDE be a investor's utility function, and it's the so-called recurse utility function. Second, we can prove that this utility function is a continue viscosity solution of the variation inequality which we get above, and we get the comparison theory. Third we can use the result to financial market to study the optimal consumption and portfolio problem or evaluate the American option. In the 4th section we study the optimal consumption and portfolio where the stock price with mixed jump-diffusion process, and get the explicit solution of this problem with maximum expected uti1ity (uti1ity function with constant coefficient and risk averseness ).In the 5th section of this thesis give an concrete example, consider optimal consumption and investment tactics with jump events, and get the optimal consumption and portfolios under maximize expected utility(risk detesting utility function with constant coefficient etc.).