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Forward-backward systems for expected utility maximization. (English) Zbl 1329.60182

Summary: In this paper, we deal with the utility maximization problem with general utility functions including power utility with liability. We derive a new approach in which we reduce the resulting control problem to the study of a system of fully-coupled forward-backward stochastic differential equations (FBSDEs) that promise to be accessible to numerical treatment.

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
93E20 Optimal stochastic control
91B16 Utility theory
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