Discrete-time approximation of decoupled forward-backward stochastic differential equations driven by pure jump lévy processes

被引：0

作者：

机构：

[1] Department of Mathematics, Faculty of Sciences Semlalia, Cadi Ayyad University, Marrakesh

来源：

Aazizi, S. (aazizi.soufiane@gmail.com) | 1600年 / Applied Probability Trust卷 / 45期

关键词：

Decoupled forward-backward SDE with jumps; Discrete-time approximation; Euler scheme; Malliavin calculus; Small jumps;

D O I：

10.1239/aap/1377868539

中图分类号：

学科分类号：

摘要：

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 e 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. © ?Applied Probability Trust 2013.

引用

页码：791 / 821

页数：30

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