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math.PR2025
Mean Field Type Control Problems Driven by Jump-diffusions
Alain Bensoussan, Ziyu Huang, Shanjian Tang +1
In this article, we apply a probabilistic approach to study general mean field type control (MFTC) problems with jump-diffusions, and give the first global-in-time solution. We all…
math.PR2024
Fractional Backward Stochastic Partial Differential Equations with Applications to Stochastic Optimal Control of Partially Observed Systems driven by Lévy Processes
Yuyang Ye, Yunzhang Li, Shanjian Tang
In this paper, we study the Cauchy problem for backward stochastic partial differential equations (BSPDEs) involving fractional Laplacian operator. Firstly, by employing the martin…
math.PR2024
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…