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September 2013 Discrete-time approximation of decoupled forward‒backward stochastic differential equations driven by pure jump Lévy processes
Soufiane Aazizi
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Adv. in Appl. Probab. 45(3): 791-821 (September 2013). DOI: 10.1239/aap/1377868539

Abstract

We present a new algorithm to discretize a decoupled forward‒backward stochastic differential equation driven by a pure jump Lévy process (FBSDEL for short). The method consists of two steps. In the first step we approximate the FBSDEL by a forward‒backward stochastic differential equation driven by a Brownian motion and Poisson process (FBSDEBP for short), in which we replace the small jumps by a Brownian motion. Then, we prove the convergence of the approximation when the size of small jumps ε goes to 0. In the second step we obtain the Lp-Hölder continuity of the solution of the FBSDEBP and we construct two numerical schemes for this FBSDEBP. Based on the Lp-Hölder estimate, we prove the convergence of the scheme when the number of time steps n goes to ∞. Combining these two steps leads to the proof of the convergence of numerical schemes to the solution of FBSDEs driven by pure jump Lévy processes.

Citation

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Soufiane Aazizi. "Discrete-time approximation of decoupled forward‒backward stochastic differential equations driven by pure jump Lévy processes." Adv. in Appl. Probab. 45 (3) 791 - 821, September 2013. https://doi.org/10.1239/aap/1377868539

Information

Published: September 2013
First available in Project Euclid: 30 August 2013

zbMATH: 1274.60216
MathSciNet: MR3102472
Digital Object Identifier: 10.1239/aap/1377868539

Subjects:
Primary: 60H35
Secondary: 60H07, 60J75

Rights: Copyright © 2013 Applied Probability Trust

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Vol.45 • No. 3 • September 2013
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