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Mutual Fund Theorem for continuous time markets with random coefficients

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  • Nikolai Dokuchaev

Abstract

We study the optimal investment problem for a continuous time incomplete market model such that the risk-free rate, the appreciation rates and the volatility of the stocks are all random; they are assumed to be independent from the driving Brownian motion, and they are supposed to be currently observable. It is shown that some weakened version of Mutual Fund Theorem holds for this market for general class of utilities; more precisely, it is shown that the supremum of expected utilities can be achieved on a sequence of strategies with a certain distribution of risky assets that does not depend on risk preferences described by different utilities.

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File URL: http://arxiv.org/pdf/0911.3194
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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 0911.3194.

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Date of creation: Nov 2009
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Publication status: Published in Theory and Decision (2014) v. 76, iss. 2, pp. 179--199
Handle: RePEc:arx:papers:0911.3194

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Web page: http://arxiv.org/

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  1. Nikolai Dokuchaev & Ulrich Haussmann, 2002. "Optimal portfolio selection and compression in an incomplete market," Papers math/0207260, arXiv.org.
  2. Walter Schachermayer & Mihai Sîrbu & Erik Taflin, 2009. "In which financial markets do mutual fund theorems hold true?," Finance and Stochastics, Springer, vol. 13(1), pages 49-77, January.
  3. Martin Kulldorff & Ajay Khanna, 1999. "A generalization of the mutual fund theorem," Finance and Stochastics, Springer, vol. 3(2), pages 167-185.
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