Weak solution for a class of fully nonlinear stochastic Hamilton–Jacobi–Bellman equations

Jinniao Qiu

Stochastic Processes and their Applications, 2017, vol. 127, issue 6, 1926-1959

Abstract: This paper is concerned with a class of stochastic Hamilton–Jacobi–Bellman equations with controlled leading coefficients, which are fully nonlinear backward stochastic partial differential equations (BSPDEs for short). In order to formulate the weak solution for such kind of BSPDEs, a class of regular random parabolic potentials are introduced in the backward stochastic framework. The existence and uniqueness of weak solution is proved, and for the partially non-Markovian case, we obtain the associated gradient estimate. As a byproduct, the existence and uniqueness of solution for a class of degenerate reflected BSPDEs is discussed as well.

Keywords: Stochastic Hamilton–Jacobi–Bellman equation; Backward stochastic partial differential equation; Weak solution; Non-Markovian control; Potential (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spa.2016.09.010

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