对共同基金定理的重新认识——不完整市场研究

本文就不完整市场提出了对连续时间共同基金定理的重新认识。这一新认识的提出同样摆脱了以往研究中对投资者消费和最终财富效用函数的假设。同样的，这些效用函数也都是可时间累加的、非减的函数。这项理论延伸也是基于离散过程和线性代数的简单属性。本文的研究结果适用于不完整市场。另外，以往只适用于包含单一风险资产的完整市场的最优投资策略自动延伸至包含多个风险资产的不完整市场。文中举出了一个实例。

A Reconsideration of Mutual Fund Theorem——A Study of Incomplete Markets

A new consideration of the continuous time mutual fund theorem in the case of incomplete market is presented, which releases traditional assumptions on the investors＇ consumption and final wealth utility functions which, however, are still time addictive and non-decreasing. This extension is built up on the basis of simple properties of diffusion processes and linear algebra. The results can be applied to incomplete markets. In addition, optimal investment strategies that used to work for complete markets with a single risky asset are proved applicable for incomplete markets with multiple risky assets. An illustrating example is examined.