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PDE solutions of stochastic differential utility. (English) Zbl 0768.90006
This paper presents conditions under which the solution of a backward stochastic differential equation in a Markovian setting can be represented as the unique solution of a particular quasi-linear parabolic (finite time case) or elliptic (infinite time case) partial differential equation. The main application is to the existence and properties of stochastic differential utility, a recursive model of preferences useful in economic theory and finance.

MSC:
91B16 Utility theory
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
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