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Quadratic BSDEs with jumps: a fixed-point approach

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1208.5581.pdf (357.9Kb)
Date
2015
Dewey
Probabilités et mathématiques appliquées
Sujet
BSDEs; quadratic growth; jumps; fixed-point theorem
Journal issue
Electronic Journal of Probability
Volume
20
Number
66
Publication date
2015
Publisher
Electronic Journal of Probability and Electronic Communications in Probability
DOI
http://dx.doi.org/10.1214/EJP.v20-3363
URI
https://basepub.dauphine.fr/handle/123456789/17185
Collections
  • CEREMADE : Publications
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Author
Kazi-Tani, Mohamed Nabil
Possamaï, Dylan
Zhou, Chao
Type
Article accepté pour publication ou publié
Abstract (EN)
In this article, we prove the existence of bounded solutions of quadratic backward SDEs with jumps, that is to say for which the generator has quadratic growth in the variables (z; u). From a technical point of view, we use a direct fixed point approach as in Tevzadze [38], which allows us to obtain existence and uniqueness of a solution when the terminal condition is small enough. Then, thanks to a well-chosen splitting, we recover an existence result for general bounded solution. Under additional assumptions, we can obtain stability results and a comparison theorem, which as usual implies uniqueness.

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