Malliavin Regularity of Non-Markovian Quadratic BSDEs and Their Numerical Schemes-Reference-Cited by-同舟云学术

Malliavin Regularity of Non-Markovian Quadratic BSDEs and Their Numerical Schemes

Published:2023-04-10 Issue:4 Volume:12 Page:366
ISSN:2075-1680
Container-title:Axioms
language:en
Short-container-title:Axioms

Author:

Doubbakh Salima¹,Khelfallah Nabil¹^ORCID,Eddahbi Mhamed²^ORCID,Almualim Anwar²

Affiliation:

1. Laboratory of Applied Mathematics, University of Biskra, P.O. Box 145, Biskra 07000, Algeria

2. Department of Mathematics, College of Sciences, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Abstract

We study both Malliavin regularity and numerical approximation schemes for a class of quadratic backward stochastic differential equations (QBSDEs for short) in cases where the terminal data need not be a function of a forward diffusion. By using the connection between the QBSDE under study and some backward stochastic differential equations (BSDEs) with global Lipschitz coefficients, we firstly prove Lq, (q≥2) existence and uniqueness results for QBSDE. Secondly, the Lp-Hölder continuity of the solutions is established for (q>4 and 2≤p<q2). Then, we analyze some numerical schemes for our systems and establish their rates of convergence. Moreover, our results are illustrated with three examples.

Funder

King Saud University

Publisher

MDPI AG

Subject

Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis

Link

https://www.mdpi.com/2075-1680/12/4/366/pdf

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