A segment-wise dynamic programming algorithm for BSDEs

TL;DR

This paper presents a new segment-wise dynamic programming algorithm for backward stochastic differential equations (BSDEs), improving computational efficiency by interpolating between existing schemes and optimizing segment length based on problem smoothness.

Contribution

The paper introduces a novel linear least-squares Monte Carlo scheme that interpolates between one-step and multi-step dynamic programming for BSDEs, with adaptive segment length for efficiency.

Findings

Algorithm reduces complexity compared to multi-step schemes

Optimal segment length depends on problem smoothness

Method interpolates between existing dynamic programming schemes

Abstract

We introduce and analyze a family of linear least-squares Monte Carlo schemes for backward SDEs, which interpolate between the one-step dynamic programming scheme of Lemor, Warin, and Gobet (Bernoulli, 2006) and the multi-step dynamic programming scheme of Gobet and Turkedjiev (Mathematics of Computation, 2016). Our algorithm approximates conditional expectations over segments of the time grid. We discuss the optimal choice of the segment length depending on the `smoothness' of the problem and show that, in typical situations, the complexity can be reduced compared to the state-of-the-art multi-step dynamic programming scheme.