Application Of A Kind Of Forward-Backward Stochastic Differential Equation In Portfolio Selection

The core of today's financial theory under conditions of uncertainty is the allocation and utilization of resources, the optimal portfolio problem, how to find the optimal portfolio strategy is an important issue, while the requirement determines the robustness of assets the need for the insurance portfolio. In the traditional research methods used in optimal control is difficult to solve complicated, and portfolio insurance strategy is not perfect, so in this paper we consider the more realistic situation of incomplete markets under the premise of using FBSDE to improve the traditional LQ model, the establishment of market conditions do not contain full portfolio model options, and then gets the optimal portfolio model strategy. In the optimal portfolio insurance strategy, we sold through the purchase of protective options, and the use of multiple copies of the joint purchase of stock and options and other strategies, the establishment of the optimal policy model and implements the investment insurance purposes. Because of in our country there is not introduction of stock options, so we study the optimal portfolio problem is much more necessary.This paper mainly divided into the following five parts:The first chapter introduces the research background and research achievements at home and abroad; the second chapter gives a coupled forward-backward stochastic differential equations existence and uniqueness proof of income and introduced the option is calculated on the log-normal distribution, To prove the last two chapters lay the foundation and calculation; third chapter gives an incomplete market case FBSDE model, and applied to the portfolio problem, obtain the optimal portfolio strategy; The fourth chapter contains two types of options portfolio insurance strategy for a systematic study, presented in more than one consisting of stock and options portfolio optimization investment model. The fifth chapter summarizes the full text, the study pointed out the shortcomings and the future direction of further development and research...