Weak Solution for a Class of Fully Nonlinear Stochastic Hamilton-Jacobi-Bellman Equations

2014/10/25 by Jinniao Qiu, Qiu, Jinniao · 1 citation
Economics, Econometrics and Finance · Mathematics · #35D30 #49L20 #60H15 #93E20 #FOS: Mathematics #Mathematical Biology Tumor Growth #Nonlinear Partial Differential Equations #Optimization and Control (math.OC) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1410.6967

openalex publication_date 2014/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is concerned with the stochastic Hamilton-Jacobi-Bellman equation with controlled leading coefficients, which is a type of fully nonlinear backward stochastic partial differential equation (BSPDE for short). In order to formulate the weak solution for such kind of BSPDEs, the classical potential theory is generalized in the backward stochastic framework. The existence and uniqueness of the 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.

Citations

• On non-Markovian forward–backward SDEs and backward stochastic PDEs

Cited by

• A Policy Iteration Scheme for Semilinear Stochastic Hamilton-Jacobi-Bellman Equations with Exponential Convergence

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