Solutions to Forward–Backward Stochastic Differential Equations with Volterra Delayed and Anticipated Terms and Applications to Optimal Control
Year: 2026
Type: article
Abstract: This paper studies a class of fully coupled forward–backward stochastic differential equations (FBSDEs in short) with Volterra delayed and anticipated terms. Such equations naturally arise in stochastic control problems involving memory effects and future-dependent terms. We establish the existence and uniqueness of adapted solutions by using the continuation method. We also discuss a linear quadratic optimal control problem with Volterra delayed terms and provide an explicit representation of the unique optimal control in terms of the solution to the associated FBSDE.
Source: Mathematics
DOI: 10.3390/math14183302
Author: Chengbo Sun
Institution: Jilin University
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W7212264403