研究了交易费用和负债情形下, 投资者与市场之间的随机微分博弈. 研究目标是: 求得最优的投资策略和市场策略最大化终值财富的期望指数效用. 使用线性二次控制理论解决了该问题, 得到了最优投资略和市场策略以及值函数的显示解. 并通过对结果进行进一步分析, 在经济上给出了一些解释.

This paper studies the problem of stochastic differential game between investor and market with transaction costs and liability. Our main goal is to find an optimal investment and market policy which maximizes the expected exponential utility of the terminal wealth. By applying linear quadratic control theory, closed-form solutions for the value function as well as the optimal investment and market policy are obtained. Finally, further explanations on the economy are given by analyzing the obtained results.