On measure solutions of backward stochastic differential equations - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2008

On measure solutions of backward stochastic differential equations

Stefan Ankirchner
  • Fonction : Auteur
Peter Imkeller
  • Fonction : Auteur
Alexandre Popier

Résumé

We consider backward stochastic differential equations (BSDE) with nonlinear generators typically of quadratic growth in the control variable. A measure solution of such a BSDE will be understood as a probability measure under which the generator is seen as vanishing, so that the classical solution can be reconstructed by a combination of the operations of conditioning and using martingale representations. In case the terminal condition is bounded and the generator fulfills the usual continuity and boundedness conditions, we show that measure solutions with equivalent measures just reinterpret classical ones. In case of terminal conditions that have only exponentially bounded moments, we discuss a series of examples which show that in case of non-uniqueness classical solutions that fail to be measure solutions can coexists with different measure solutions.

Dates et versions

hal-00373487 , version 1 (06-04-2009)

Identifiants

Citer

Stefan Ankirchner, Peter Imkeller, Alexandre Popier. On measure solutions of backward stochastic differential equations. 2008. ⟨hal-00373487⟩
128 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More