Path regularity and explicit convergence rate for BSDE with truncated quadratic growth

Peter Imkeller, Goncalo Dos Reis*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We consider backward stochastic differential equations with drivers of quadratic growth (qgBSDE). We prove several statements concerning path regularity and stochastic smoothness of the Solution processes of the qg-BSDE, in particular we prove an extension of Zhang's path regularity theorem to the quadratic growth setting. We give explicit convergence rates for the difference between the Solution of a qgBSDE and its truncation, filling an important gap in numerics for qgBSDE. We give ail alternative proof of second order Malliavin differentiability for BSDE with drivers that are Lipschitz continuous (and differentiable), and then derive ail analogous result for qgBSDE. (C) 2009 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)348-379
Number of pages32
JournalStochastic processes and their applications
Volume120
Issue number3
DOIs
Publication statusPublished - Mar 2010

Keywords

  • BSDE
  • Driver of quadratic growth
  • Malliavin calculus
  • Path regularity
  • BMO martingales
  • Numerical scheme
  • Truncation
  • STOCHASTIC DIFFERENTIAL-EQUATIONS

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