Reflected backward stochastic differential equation with jumps and random obstacle
type: Item
instance of: scholarly article
title: Reflected backward stochastic differential equation with jumps and random obstacle
zbMATH Open document ID: 1015.60051
published in: Electronic Journal of Probability
publication date: 2003-02-13T00:00:00Z
full work available at URL: https://eudml.org/doc/122750
review text: Reflected backward stochastic differential equations (BSDE in short) were introduced by \textit{N. El Karoui}, \textit{C. Kapoudjian}, \textit{E. Pardoux}, \textit{S. Peng} and \textit{M. C. Quenez} [Ann. Probab. 25, No. 2, 702-737 (1997; Zbl 0899.60047)]. The authors of the present paper study a one-dimensional reflected BSDE whose noise is driven by a Brownian motion and an independent Poisson random measure. By two methods -- by penalization and by the Snell envelope theory -- plus some fix point arguments, they show that existence and uniqueness of a solution hold. Further they make the link between these reflected BSDEs and integro-differential mixed stochastic optimal control.
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60H20
Mathematics Subject Classification ID: 60H99
zbMATH DE Number: 1868604
zbMATH Keywords: backward stochastic differential equation
zbMATH Keywords: penalization
zbMATH Keywords: Poisson point process
zbMATH Keywords: martingale representation theorem
zbMATH Keywords: integral-differential mixed control
author: Said Hamadène
author: Youssef Ouknine
reviewed by: Catherine Rainer
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1868604