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.
Peng,Stochastic Hamilton–Jacobi–Bellman equations, SIAM J
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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.