摘要翻译：
在一个具有有限时间范围T的一般半鞅金融市场S中，考虑了共同基金定理(MFT)，其中代理人的最终财富期望效用最大化。建立了：1）设N是num\'eraire投资组合的财富过程（即。log实用工具的最优投资组合）。如果写在num\'eraire投资组合上的具有到期日T的路径无关期权可以通过在N中交易\emph{only}来复制，那么对于一般效用函数(MFT)成立，并且num\'eraire投资组合可以作为共同基金。这推广了默顿关于Black-Scholes市场的经典结果。相反，在一个补充的弱完备性假设下，我们证明了对于一般效用函数(MFT)的有效性蕴涵了对于上述的Num\'eraire投资组合的期权同样的可复制性。2）如果对于给定的一类效用函数（即。在所有完全布朗金融市场S中，投资者的MFTT都成立，那么所有投资者使用的效用函数U一定是HARA型的，这是Cass和Stiglitz经典工作精神的结果。
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英文标题：
《In which Financial Markets do Mutual Fund Theorems hold true?》
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作者：
Walter Schachermayer, Mihai Sirbu and Erik Taflin
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最新提交年份：
2007
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Trading and Market Microstructure        交易与市场微观结构
分类描述：Market microstructure, liquidity, exchange and auction design, automated trading, agent-based modeling and market-making
市场微观结构，流动性，交易和拍卖设计，自动化交易，基于代理的建模和做市
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一级分类：Mathematics        数学
二级分类：Optimization and Control        优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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英文摘要：
  The Mutual Fund Theorem (MFT) is considered in a general semimartingale financial market S with a finite time horizon T, where agents maximize expected utility of terminal wealth. It is established that:   1) Let N be the wealth process of the num\'eraire portfolio (i.e. the optimal portfolio for the log utility). If any path-independent option with maturity T written on the num\'eraire portfolio can be replicated by trading \emph{only} in N, then the (MFT) holds true for general utility functions, and the num\'eraire portfolio may serve as mutual fund. This generalizes Merton's classical result on Black-Scholes markets.   Conversely, under a supplementary weak completeness assumption, we show that the validity of the (MFT) for general utility functions implies the same replicability property for options on the num\'eraire portfolio described above.   2) If for a given class of utility functions (i.e. investors) the (MFT) holds true in all complete Brownian financial markets S, then all investors use the same utility function U, which must be of HARA type. This is a result in the spirit of the classical work by Cass and Stiglitz.
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PDF链接：
https://arxiv.org/pdf/0710.1909