Bernoulli

  • Bernoulli
  • Volume 26, Number 1 (2020), 159-190.

Random walk approximation of BSDEs with Hölder continuous terminal condition

Christel Geiss, Céline Labart, and Antti Luoto

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Abstract

In this paper, we consider the random walk approximation of the solution of a Markovian BSDE whose terminal condition is a locally Hölder continuous function of the Brownian motion. We state the rate of the $L_{2}$-convergence of the approximated solution to the true one. The proof relies in part on growth and smoothness properties of the solution $u$ of the associated PDE. Here we improve existing results by showing some properties of the second derivative of $u$ in space.

Article information

Source
Bernoulli, Volume 26, Number 1 (2020), 159-190.

Dates
Received: September 2018
Revised: February 2019
First available in Project Euclid: 26 November 2019

Permanent link to this document
https://projecteuclid.org/euclid.bj/1574758825

Digital Object Identifier
doi:10.3150/19-BEJ1120

Mathematical Reviews number (MathSciNet)
MR4036031

Zentralblatt MATH identifier
07140496

Keywords
backward stochastic differential equations numerical scheme random walk approximation speed of convergence

Citation

Geiss, Christel; Labart, Céline; Luoto, Antti. Random walk approximation of BSDEs with Hölder continuous terminal condition. Bernoulli 26 (2020), no. 1, 159--190. doi:10.3150/19-BEJ1120. https://projecteuclid.org/euclid.bj/1574758825


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