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Explicit Formulae for Power Utility Maximization Problems

Abstract:
We consider the problem of expected power utility maximization from terminal wealth in di ffusion market models under partial information. Explicit expressions for the value-process and for the optimal strategy are obtained for some interesting special cases. In particular, a closed form solution is given in terms of a PDE with terminal condition for Markovian models. An illustration of the optimal strategy is provided by means of some numerical simulations.

Keywords:
Backward stochastic di fferential equation; power utility maximization problem; basis risk model; stochastic correlation

MSC:
60