Fractional backward stochastic differential equations with delayed generator

TL;DR

This paper investigates the existence, uniqueness, and comparison properties of fractional backward stochastic differential equations with generators that depend on current and past solution values, expanding the theoretical understanding of such equations.

Contribution

It introduces new results on the solvability and comparison theorems for fractional BSDEs with delayed generators under Lipschitz conditions.

Findings

Existence and uniqueness of solutions established

Comparison theorem proved for these BSDEs

Framework extends understanding of fractional BSDEs with delays

Abstract

In this paper, we focus on the solvability of a class of fractional backward stochastic differential equations (BSDEs, for short) with delayed generator. In this class of equations, the generator includes not only the values of the solutions of the present but also the past. Under Lipschitz condition, the existence and uniqueness of such BSDEs are established. A comparison theorem for this class of BSDEs is also obtained.