Viscosity Solutions of Stochastic Hamilton--Jacobi--Bellman Equations
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Publication:4691148
DOI10.1137/17M1148232zbMATH Open1401.49030arXiv1709.06143MaRDI QIDQ4691148
Author name not available (Why is that?)
Publication date: 18 October 2018
Published in: (Search for Journal in Brave)
Abstract: In this paper we study the fully nonlinear stochastic Hamilton-Jacobi-Bellman (HJB) equation for the optimal stochastic control problem of stochastic differential equations with random coefficients. The notion of viscosity solution is introduced, and we prove that the value function of the optimal stochastic control problem is the maximal viscosity solution of the associated stochastic HJB equation. For the superparabolic cases when the diffusion coefficients are deterministic functions of time, states and controls, the uniqueness is addressed as well.
Full work available at URL: https://arxiv.org/abs/1709.06143
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