Forward Backward Stochastic Differential Equations - Asymptotics and a Large Deviations Principle

TL;DR

This paper investigates the asymptotic behavior of solutions to coupled forward-backward stochastic differential equations under small perturbations and establishes a large deviation principle for their laws.

Contribution

It introduces new asymptotic analysis for coupled FBSDEs with small multiplicative noise and proves a large deviation principle for the process laws.

Findings

Asymptotic behavior characterized for small perturbations

Large deviation principle established for the process laws

Insights into stability and rare events in FBSDEs

Abstract

We study the asymptotic behaviour of solutions of Forward Backward Stochastic Differential Equations in the coupled case, when the diffusion coefficient of the forward equation is multiplicatively perturbed by a small parameter that converges to zero. Furthermore, we establish a Large Deviation Principle for the laws of the corresponding processes.