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math.PR2024★ 1 cited
Viscosity Solutions of Second Order Path-Dependent Partial Differential Equations and Applications
Shanjian Tang, Jianjun Zhou
In this article, a notion of viscosity solutions is introduced for fully nonlinear second order path-dependent partial differential equations in the spirit of [Zhou, Ann. Appl. Pro…
math.OC2024★ 1 cited
Optimal Control of Unbounded Functional Stochastic Evolution Systems in Hilbert Spaces: Second-Order Path-dependent HJB Equation
Shanjian Tang, Jianjun Zhou
Optimal control and the associated second-order path-dependent Hamilton-Jacobi-Bellman (PHJB) equation are studied for unbounded functional stochastic evolution systems in Hilbert…
math.OC2024★ 3 cited
Viscosity Solutions for HJB Equations on the Process Space
Jianjun Zhou, Nizar Touzi, Jianfeng Zhang
In this paper we investigate a path dependent optimal control problem on the process space with both drift and volatility controls, with possibly degenerate volatility. The dynamic…