Non-Markovian Fully Coupled Forward-Backward Stochastic Systems and Classical Solutions of Path-dependent PDEs

2012/04/16 by Shaolin Ji, Ji, Shaolin, Shuzhen Yang +1
Decision Sciences · Economics, Econometrics and Finance · #Analysis of PDEs (math.AP) #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1204.3351

openalex publication_date 2012/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper explores the relationship between non-Markovian fully coupled forward-backward stochastic systems and path-dependent PDEs. The definition of classical solution for the path-dependent PDE is given within the framework of functional Itô calculus. Under mild hypotheses, we prove that the forward-backward stochastic system provides the unique classical solution to the path-dependent PDE.

Citations

• Conjugate convex functions in optimal stochastic control

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