Optimal Investments for Robust Utility Functionals in Complete Market Models
Optimal Investments for Robust Utility Functionals in Complete Market Models
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DOI：
10.1287/moor.1040.0138
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发表时间：
2005-08
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影响因子：
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通讯作者：
A. Schied
中科院分区：
文献类型：
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作者：
A. Schied
本文介绍了一种系统方法，用于解决在一般完整市场模型中最大化可接受策略的终端财富的鲁棒效用问题，其中鲁棒效用函数由一组 Q 概率度量来定义。我们的主要结果表明，这个问题通常可以简化为确定“最不有利”的度量 Q0→Q，这是普遍的，因为它不依赖于特定的效用函数。因此，鲁棒问题相当于关于“主观”概率度量 Q0 的标准效用最大化问题。通过使用鲁棒统计中的 Huber-Strassen 定理，表明如果 Q 是 2-交替容量的 I-核，则 Q0 始终存在。除了其他例子之外，我们还讨论了布莱克-斯科尔斯市场中具有不确定漂移的鲁棒效用最大化问题以及“弱信息”的情况。
This paper introduces a systematic approach to the problem of maximizing the robust utility of the terminal wealth of an admissible strategy in a general complete market model, where the robust utility functional is defined by a set Q of probability measures. Our main result shows that this problem can often be reduced to determining a "least favorable" measure Q0âQ, which is universal in the sense that it does not depend on the particular utility function. The robust problem is thus equivalent to a standard utility-maximization problem with respect to the "subjective" probability measure Q0. By using the Huber-Strassen theorem from robust statistics, it is shown that Q0 always exists if Q is the I-core of a 2-alternating capacity. Besides other examples, we also discuss the problem of robust utility maximization with uncertain drift in a Black-Scholes market and the case of "weak information."