Deep BSDE Solver on Bounded Domains Part I: General Loss Rate

TL;DR

This paper develops a deep BSDE solver tailored for bounded domains with random horizons, providing a convergence rate based on discretization and approximation metrics.

Contribution

It introduces a generalized loss functional for deep BSDEs on bounded domains and derives a convergence rate for a class of weighted modifications.

Findings

Convergence rate expressed in terms of stepsize and approximation distance.

Applicable to BSDEs with random, unbounded time horizons.

Provides theoretical guarantees for the deep BSDE solver on bounded domains.

Abstract

We consider a ramification of the deep BSDE loss functional designed to apply for BSDEs on bounded domains, i.e. with random (unbounded) time horizons. We derive a general convergence rate of the loss functional; precisely for a class of (randomly) weighted modifications of the functional. The rate is expressed in terms of the underlying discrete-time stepsize and a universal approximation distance.