Stochastic Control and Differential Games with Path-Dependent Influence of Controls on Dynamics and Running Cost

2016/11/02 by Yuri F. Saporito, Saporito, Yuri F.
Economics, Econometrics and Finance · Mathematics · #49L99 #60H30 #91A15 #Climate Change Policy and Economics #Economic theories and models #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR) #Stochastic processes and financial applications #math.OC #math.PR #msc:49L99 #msc:60H30 #msc:91A15

paper · pdf · doi:10.48550/arxiv.1611.00589

15 pages, 3 figures

openalex publication_date 2016/11/02 · arxiv created 2019/02/08 · arxiv updated 2019/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the functional Itô calculus framework to find a path-dependent version of the Hamilton-Jacobi-Bellman equation for stochastic control problems that feature dynamics and running cost that depend on the path of the control. We also prove a Dynamic Programming Principle for such problems. We apply our results to path-dependence of the delay type. We further study Stochastic Differential Games in this context.

Citations

• Systemic Risk and Stochastic Games with Delay

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