Abstract:The Euler scheme is a standard time discretization for BSDEs, but its implementation hinges on approximating conditional expectations and the associated martingale terms at each time step. We propose an implementation based on the Wiener chaos decomposition to approximate these quantities. In contrast to many numerical schemes that rely on a finite-dimensional Markovian representation, our approach accommodates arbitrary $\mathcal{F}_T$-measurable square-integrable terminal conditions. We provide a comprehensive convergence analysis under additional Malliavin regularity assumptions and illustrate the method on several numerical examples, including genuinely non-Markovian problems arising, for instance, in the pricing and hedging of contingent claims under rough-volatility models.
From: Pere Diaz-Lozano [view email]
[v1]
Thu, 18 Dec 2025 11:14:13 UTC (1,342 KB)
[v2]
Mon, 22 Jun 2026 12:34:46 UTC (1,645 KB)
[v3]
Fri, 4 Sep 2026 15:29:12 UTC (2,942 KB)
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