# Backward SDE Representation for Stochastic Control Problems with Non Dominated Controlled Intensity

Abstract : We are interested in stochastic control problems coming from mathematical finance and, in particular, related to model uncertainty, where the uncertainty affects both volatility and intensity. This kind of stochastic control problems is associated to a fully nonlinear integro-partial differential equation, which has the peculiarity that the measure $(\lambda(a,\cdot))_a$ characterizing the jump part is not fixed but depends on a parameter $a$ which lives in a compact set $A$ of some Euclidean space $\R^q$. We do not assume that the family $(\lambda(a,\cdot))_a$ is dominated. Moreover, the diffusive part can be degenerate. Our aim is to give a BSDE representation, known as nonlinear Feynman-Kac formula, for the value function associated to these control problems. For this reason, we introduce a class of backward stochastic differential equations with jumps and partially constrained diffusive part. We look for the minimal solution to this family of BSDEs, for which we prove uniqueness and existence by means of a penalization argument. We then show that the minimal solution to our BSDE provides the unique viscosity solution to our fully nonlinear integro-partial differential equation.
Keywords :
Type de document :
Pré-publication, Document de travail
2014
Domaine :
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https://hal.archives-ouvertes.fr/hal-00991109
Contributeur : Andrea Cosso <>
Soumis le : mercredi 14 mai 2014 - 17:11:36
Dernière modification le : lundi 29 mai 2017 - 14:26:00
Document(s) archivé(s) le : jeudi 14 août 2014 - 12:05:33

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### Identifiants

• HAL Id : hal-00991109, version 1
• ARXIV : 1405.3540

### Citation

Sébastien Choukroun, Andrea Cosso. Backward SDE Representation for Stochastic Control Problems with Non Dominated Controlled Intensity. 2014. <hal-00991109>

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