证券市场中庄家与散户间的确定性微分博弈

Deterministic differential game of individual market makers in securities market

基于确定性微分博弈理论,建立了一种庄家与散户间的连续时间的博弈模型.首先将所有散户作为一个整体与庄家进行博弈,以博弈双方持股率的动态关系作为动态系统方程,并以此构建了一个确定性微分博弈模型;然后运用开环纳什均衡和反馈纳什均衡分别求解出满足共态函数的常微分方程组和满足价值函数的Issacs-Bellman偏微分方程,以此得到庄家与散户博弈的开环纳什均衡策略和反馈纳什均衡策略.该结果可为金融监管部门监管证券市场和证券市场投资者买卖股票提供参考.

Based on the theory of deterministic differential game,a continuous time game model between the dealer and the retail investor is established.Firstly,all retail investors are regarded as a whole to play a game with the makers,and the dynamic relationship of the shareholding ratio of the two sides in the game is regarded as the dynamic system equation;Then,the open-loop Nash equilibrium and the feedback Nash equilibrium are used to solve the ordinary differential equations satisfying the common state function and the Issacs Bellman partial differential equations satisfying the value function,respectively,so as to obtain the open-loop Nash equilibrium strategy and the feedback Nash equilibrium strategy of the game between the dealer and the retail investor.The results can provide a reference for financial regulators to supervise the securities market and investors to buy and sell stocks in the securities market.