带交易费用和负债的均值-方差投资策略选择

Mean-Variance Portfolio Selection with Transaction Costs and Liability

研究了均值-方差准则下,带交易费用和负债的投资组合选择问题.研究目标是,在终值财富的均值等于d的限制下,使终值财富的方差最小,即均值-方差组合选择问题.通过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和有效边界的显式解.并通过对所得结果进行进一步分析及实例,在经济上给出了合理的解释.通过本文的研究,可以指导投资者在具有负债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.

Investment portfolio selection problem with transaction costs and liability is considered under meanvariance criterion. The main goal is to minimize the variance of the terminal wealth under the constraint that terminal wealth is equivalent to d,namely,the mean-variance portfolio selection problem. Applying linear-quadratic theory,optimal investment strategies as well as the mean-variance valid frontier are then analytically derived.Meanwhile,according to the further analysis and practical example,an explanation in economy is given. This research could be adopted by investors with liability to select the appropriate investment strategy for more wealth while minimizing the risk.