2024/12/11 by Rhoss Likibi Pellat, Pellat, Rhoss Likibi, Emmanuel Fonka +3 · 1 citation
Economics, Econometrics and Finance · #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2412.08497
We investigate the convergence rate for the time discretization of a class of quadratic backward SDEs -- potentially involving path-dependent terminal values -- when coupled with non-standard Lipschitz-type forward SDEs. In our review of the explicit time-discretization schemes in the spirit of Pagès & Sagna (see \citePaSa18), we achieve an error control close to (1)/(2), even under the modest assumptions considered in this work (see \citeChaRichou16, for comparison). A central element of our approach is a thorough re-examination of Zhang's L2-time regularity of the martingale integrand Z which follows from an extension of the first-order variational regularity for this class of singular forward-backward SDEs with non-uniform Cauchy-Lipschitz drivers. This is complemented by the recently introduced caracterisation of stochastic processes of \it bounded mean oscillation (abbreviated as \bmo) by K. Lê (see \citeLe22) which we used to derive an Lp-version of the strong approximation of SDEs with singular drifts from Dareiotis & Gerencsér (see \citeDaGe20). As such, this study addresses a crucial gap in the numerical analysis of forward-backward SDEs (FBSDEs). To our knowledge, for the first time, the impact of regularization by noise on Euler-Maruyama numerical schemes for singular forward SDEs has been successfully transferred to enhance the convergence rate of the discrete time approximations for solutions to backward SDEs.