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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