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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.
We study the stochastic differential game between investors and the market in the case of transaction costs and liabilities.The objective of the research is to find out the optimal index strategy and market strategy to maximize the exponential utility of the ultimate value of wealth.Using linear quadratic control theory This problem is solved, and the optimal solution of investment, market strategy and the display of value function are obtained, and some explanations are provided economically through the further analysis of the result.