Nonparametric estimation of FBSDEs with random terminal time

TL;DR

This paper develops nonparametric methods for estimating functional coefficients in FBSDEs with random terminal time, providing asymptotic analysis and empirical likelihood-based confidence intervals.

Contribution

It introduces a comprehensive nonparametric estimation framework for FBSDEs with random terminal time, including asymptotic results and a novel empirical likelihood approach.

Findings

Asymptotic distributions characterized in two dimensions

Empirical likelihood method effectively constructs confidence intervals

Numerical simulations demonstrate finite-sample performance

Abstract

This paper investigates the nonparametric estimation of the functional coefficients of the FBSDEs with random terminal time, including the local constant and local linear estimators. We provide complete two-dimensional asymptotics in both the time span and the sampling interval, allowing for the precise characterization of their distribution. Moreover, the empirical likelihood (EL) method to construct the data-driven confidence intervals for these estimators is provided. Some numerical simulations investigate the finite-sample properties of the estimators and compare the performance of the EL method and the conventional method in constructing confidence intervals based on asymptotic normality.