Mutual Fund Theorem for continuous time markets with random coefficients

Details Mutual Fund Theorem for continuous time markets with random coefficients Mutual Fund Theorem for continuous time markets with random coefficients

2009-11-17

arxiv.org/abs/0911.3194v1

Economy

Quantitative Finance

Portfolio Management

17 pages

Scientific paper

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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