• français
    • English
  • English 
    • français
    • English
  • Login
JavaScript is disabled for your browser. Some features of this site may not work without it.
BIRD Home

Browse

This CollectionBy Issue DateAuthorsTitlesSubjectsJournals BIRDResearch centres & CollectionsBy Issue DateAuthorsTitlesSubjectsJournals

My Account

Login

Statistics

View Usage Statistics

Second order backward stochastic differential equations with quadratic growth

Thumbnail
Date
2013
Link to item file
http://arxiv.org/abs/1201.1050v4
Dewey
Probabilités et mathématiques appliquées
Sujet
Second order backward stochastic differential equation; Quadratic growth; BMO martingales; r.c.p.d.; Feynman–Kac; Fully non-linear PDEs; Quasi-sure
Journal issue
Stochastic Processes and their Applications
Volume
123
Number
10
Publication date
2013
Article pages
3770-3799
Publisher
Elsevier
DOI
http://dx.doi.org/10.1016/j.spa.2013.05.007
URI
https://basepub.dauphine.fr/handle/123456789/14888
Collections
  • CEREMADE : Publications
Metadata
Show full item record
Author
Possamaï, Dylan
Zhou, Chao
Type
Article accepté pour publication ou publié
Abstract (EN)
We extend the well posedness results for second order backward stochastic differential equations introduced by Soner, Touzi and Zhang (2012) [31] to the case of a bounded terminal condition and a generator with quadratic growth in the zz variable. More precisely, we obtain uniqueness through a representation of the solution inspired by stochastic control theory, and we obtain two existence results using two different methods. In particular, we obtain the existence of the simplest purely quadratic 2BSDEs through the classical exponential change, which allows us to introduce a quasi-sure version of the entropic risk measure. As an application, we also study robust risk-sensitive control problems. Finally, we prove a Feynman–Kac formula and a probabilistic representation for fully non-linear PDEs in this setting.

  • Accueil Bibliothèque
  • Site de l'Université Paris-Dauphine
  • Contact
SCD Paris Dauphine - Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16

 Content on this site is licensed under a Creative Commons 2.0 France (CC BY-NC-ND 2.0) license.