Weak solutions of backward stochastic differential equations with continuous generator

Nadira Bouchemella and Paul Raynaud de Fitte

Stochastic Processes and their Applications, 2014, vol. 124, issue 1, 927-960

Abstract: We prove the existence of a weak solution to a backward stochastic differential equation (BSDE) Yt=ξ+∫tTf(s,Xs,Ys,Zs)ds−∫tTZsdWs in a finite-dimensional space, where f(t,x,y,z) is affine with respect to z, and satisfies a sublinear growth condition and a continuity condition. This solution takes the form of a triplet (Y,Z,L) of processes defined on an extended probability space and satisfying Yt=ξ+∫tTf(s,Xs,Ys,Zs)ds−∫tTZsdWs−(LT−Lt) where L is a martingale with possible jumps which is orthogonal to W. The solution is constructed on an extended probability space, using Young measures on the space of trajectories. One component of this space is the Skorokhod space D endowed with the topology S of Jakubowski.

Keywords: Weak solution; Joint solution measure; Young measure; Jakubowski’s topology S; Condition UT; Meyer–Zheng; Yamada–Watanabe–Engelbert (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304414913002482
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:124:y:2014:i:1:p:927-960

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spa.2013.09.011

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().