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A discrete-time approximation for doubly reflected BSDEs

Part of: Stochastic processes Stochastic analysis Probabilistic methods, simulation and stochastic differential equations

Published online by Cambridge University Press:  01 July 2016

Jean-François Chassagneux
Jean-François Chassagneux*
Affiliation:
Université Paris Diderot - Paris 7, PMA, and ENSAE-CREST
*
∗ Postal address: ENSAE, Timbre J120, 3 avenue Pierre Larousse, 92245 Malakoff Cedex, France. Email address: [email protected]
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Abstract

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We study the discrete-time approximation of doubly reflected backward stochastic differential equations (BSDEs) in a multidimensional setting. As in Ma and Zhang (2005) or Bouchard and Chassagneux (2008), we introduce the discretely reflected counterpart of these equations. We then provide representation formulae which allow us to obtain new regularity results. We also propose an Euler scheme type approximation and give new convergence results for both discretely and continuously reflected BSDEs.

Keywords

Reflected BSDEsdiscrete-time approximation schemesgame optionregularity

MSC classification

Primary: 65C99: None of the above, but in this section 60H35: Computational methods for stochastic equations 60G40: Stopping times; optimal stopping problems; gambling theory
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 41 , Issue 1 , March 2009 , pp. 101 - 130
Copyright
Copyright © Applied Probability Trust 2009 

Footnotes

The author would like to thank Bruno Bouchard for fruitful discussions.

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