The Application Of HJB Equation In Disposable Option And Stock Trading Strategy

In financial engineering literature, trading rules of option, stock and other securities are main-ly related to the settlement of securities derivatives within a short time. This rule is practically feasible only when a small amount of the securities business involved. In fact, selling a lot of stock in a short period of time will cause the overall stock market crashing and shares tumbling. In this article, the writer considers to achieve the sales volume of securities in a long period, by the means of selling a small amount of securities time and again. Particularly, the number of financial tools is, in a sense, continuously changing and the corresponding settlement is decided by the selling rate. And that is why we use the flow model to deal with the liquidation problem. Our goal is to maximize the expected return. Potential problems can be described as a stochastic control problem with state limiting. Method for limiting viscosity solutions is used to describe the optimal return function and dynamic problems with relevant boundary conditions. At last, through numerical solution, we study the relationship between strategy、pricing and the parameters.This paper consists of four chapters. The first chapter introduces the research background and literature review. The second chapter mainly introduces the Deduction of a Wiener process, the Ito formula, the principle of dynamic programming and HJB equation. The third chapter studies the application of HJB equation in the defaultable options trading strategies, and obtains numerical results. The fourth chapter studies the application of HJB equation in the stock trading strategies, and numerical results are obtained.