Convergence of BSEs driven by random walks to BSDEs: The case of (in)finite activity jumps with general driver

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• 作者：Dilip Madan^a ; ^{dbm@rhsmith.umd.edu" class="auth_mail" title="E-mail the corresponding author} ; Martijn Pistorius^b ; ^{m.pistorius@imperial.ac.uk" class="auth_mail" title="E-mail the corresponding author} ; Mitja Stadje^c ; ^{mitja.stadje@uni-ulm.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：60H10 ; 60Fxx
• 刊名：Stochastic Processes and their Applications
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：126
• 期：5
• 页码：1553-1584
• 全文大小：359 K

文摘

In this paper we present a weak approximation scheme for BSDEs driven by a Wiener process and an (in)finite activity Poisson random measure with drivers that are general Lipschitz functionals of the solution of the BSDE. The approximating backward stochastic difference equations (BS5003026&_mathId=si1.gif&_user=111111111&_pii=S0304414915003026&_rdoc=1&_issn=03044149&md5=34228fa37b887aea9bc59bf13d63fbba">5003026-si1.gif">$\Delta$Es) are driven by random walks that weakly approximate the given Wiener process and Poisson random measure. We establish the weak convergence to the solution of the BSDE and the numerical stability of the sequence of solutions of the BS5003026&_mathId=si1.gif&_user=111111111&_pii=S0304414915003026&_rdoc=1&_issn=03044149&md5=34228fa37b887aea9bc59bf13d63fbba">5003026-si1.gif">$\Delta$Es. By way of illustration we analyze explicitly a scheme with discrete step-size distributions.