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Volume 17,     Number 4,     Winter 2009

 

TIME CONSISTENT UTILITY MAXIMIZATION
TRAIAN A. PIRVU AND ULRICH G. HAUSSMANN

Abstract. This paper studies the problem of optimal investment in incomplete markets, time consistent with respect to stopping times investment horizons. We work in a Brownian motion framework and the stopping times are adapted to the Brownian filtration. Time consistency is achieved only if the risk preferences are time and state dependent. Thus, they are utilities random fields. Starting with a time and state independent utility we construct a utility random field which leads to optimal time consistent investment. As an application to the classical utility theory we provide a portfolio decomposition formula.

 

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