Two Kinds Of Models In Mean-Variance Portfolio Games

Abstract:Mathematic finance is an emerging and frontier discipline, which is the intersection of finance and mathematics and an important part of contemporary finance. In the course of the game, both players use different investment strategies to reach the so-called "win-win" situation, maximizing benefits, achieving the best result of the game. In reality, we tend to choose different strategies based on the specific situation. Meanwhile, we have to consider the strategy that our opponent may take. Since the application of game theory has so much practical significance, we should consider promoting the application of the game theory in the financial market.This paper studies the problem of stochastic differential portfolio including a risk-free asset and two risky assets simply composed by two investors in financial market. Firstly, by using dynamic programming principle (HJB equation), we study the optimal strategy and its value function for the two investors in their risk aversion with minimum risks and maximum simple financial market total assets when the price process obeys CEV process. We give some sensitivity analysis of parameters and numerical simulation, as well as their economic significance. Secondly, we study the optimal strategy and its value function for the two investors in their risk aversion with minimum risks and maximum simple financial market total assets when the price process obeys O-U process.