均值-方差准则下具有负债的随机微分博弈

研究了均值-方差准则下，具有负债的随机微分博弈.研究目标是：在终值财富的均值等于k的限制下，在市场出现最坏的情况下找到最优的投资策略使终值财富的方差最小.即：基于均值-方差随机微分博弈的投资组合选择问题.使用线性-二次控制的理论解决了该问题，获得了最优的投资策略、最优市场策略和有效边界的显示解.并通过对所得结果进行进一步分析，在经济上给出了进一步的解释.通过本文的研究，可以指导金融公司在面临负债和金融市场情况恶劣时，选择恰当的投资策略使自身获得一定的财富而面临的风险最小.

Stochastic Differential Games under Mean-variance Criterion with Liability

This paper studied the stochastic differential games with liability under mean-variance criterion. Assuming that the market is the worst and the constraint that terminal wealth is equivalent to k, this paper obtained the optimal investment strategies, which minimized the variance of the terminal wealth, i.e. the mean-variance portfolio selection problem with stochastic differential games. Through applying linear-quadratic theory to solve this problem, the optimal investment strategies and optimal market strategies as well as the mean-variance efficient frontier were then analytically derived. And through analyzing the results, a further explanation on the economy was given. When facing liability and financial market downturn, this paper can guide financial company to select the appropriate investment strategy to gain some wealth meanwhile minimizing the risk.