Establishes a stochastic viscosity solution framework using semimartingale test functions for BSHJB equations with jumps, proving DPP, existence via measurable selection and Ito-Kunita formula, and uniqueness under super-parabolicity.
Path-Dependent Optimal Stochastic Control and Viscosity Solution of Associated Bellman Equations
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abstract
In this paper we study the optimal stochastic control problem for a path-dependent stochastic system under a recursive path-dependent cost functional, whose associated Bellman equation from dynamic programming principle is a path-dependent fully nonlinear partial differential equation of second order. A novel notion of viscosity solutions is introduced. Using Dupire's functional It\^o calculus, we characterize the value functional of the optimal stochastic control problem as the unique viscosity solution to the associated path-dependent Bellman equation.
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math.OC 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Viscosity Solutions of Stochastic Hamilton--Jacobi--Bellman Equations with Jumps
Establishes a stochastic viscosity solution framework using semimartingale test functions for BSHJB equations with jumps, proving DPP, existence via measurable selection and Ito-Kunita formula, and uniqueness under super-parabolicity.