Forward-backward stochastic differential equation is a very important tool for solving stochastic control problems, and fractional Brownian motion has properties such as long-term memory and self-similarity.
Therefore, the study of fractional forward-backward stochastic differential equations which are widely used in financial mathematics is extensively studied.
The continuation method is one of the important approaches to study forward-backward stochastic differential equations.
In the previous study, authors have proved the existence and uniqueness of solutions for forward-backward stochastic differential equations driven by Brownian motion with delay and anticipated terms using the estimates of solutions for the anticipated backward stochastic differential equations. The authors also obtained the existence and uniqueness of solutions for fractional mean-field anticipated backward stochastic differential equations and studied the related stochastic control problem.
We have proved the unique existence of solutions for fully coupled fractional forward-backward stochastic differential equations with delay and anticipated terms using the continuous method.
Our research results were published in "Statistics and Probability Letters" under the title of "Existence and uniqueness of solution for full coupled fractional forward-backward stochastic equations with delay and anticipated term"(https://doi.org/10.1016/j.spl.2023.109954).
