Stochastic Differential Games In The Financial Market And Oil Market

Mathematic finance is an interactive subject to probe derivatives in the financial market using mathematic method, with portfolio selection as a great part in its content. In the real world, our decisions should be made on the consideration of other’s corresponding responds. Hence the study of decision making in an interactive environment can be seen as a game behavior which is often investigated by game theory. On the other hand, decisions made by investors usually vary from time to time, namely, the decisions change dynamically. Therefore, it is quite reasonable to apply stochastic differential game theory in modeling and solving such dynamic optimal portfolio selection problems.In this essay, we first give the basic theory and concept in chapter1and2, then in chapter3we deal with the dynamic game theory in the financial market in which the price of stock are governed by CEV model and OU model respectively. At the same time we also discuss these respective portfolio selections in both models. Using stochastic linear quadratic control method and dynamic programming method, we can derive the corresponding strategies and the value functions in both cases.In the following chapter, we apply game theory in the more practical case, specifically oil market, we aim to investigate the exploitation of oil field and the competition between two duopoly companies. In both cases, we need to give the respective perfect strategies in non-cooperative game and cooperative games. The corresponding value functions are also given in different cases. At the same time, we know that the exploitation of oil has the priority, which is best known as leader-follower problem. In the last chapter, when the oil company has the stock, we give the descriptions of an measurement of the risk, specifically, the earnings at risk and capital at risk of the stock, and then derive the optimal portfolio strategy and the corresponding expectations.