HAL : hal-00515522, version 3

Fiche détaillée

Récupérer au format BibTeX - EndNote - TEI - RefWorks -

Versions disponibles :

v1 (07-09-2010)

v2 (16-12-2010)

v3 (17-08-2011)

Stochastic target problems with controlled loss in jump diffusion models

Ludovic Moreau 1

(01/07/2010)

In this paper, we consider a mixed diffusion version of the stochastic target problem introduced by Bouchard et al. (2009). This consists in finding the minimum initial value of a controlled process which guarantees to reach a controlled stochastic target with a given lovel of expected loss. As in Bouchard et al. (2009), it can be converted into a standard stochastic target problem, as already studied by Soner and Touzi (2002) or Bouchard (2002) for the mixed diffusion case, by increasing both the state space and the dimension of the control. In our mixed-diffusion setting, the main difficulty comes from the presence of jumps, which leads to the introduction of a new kind of controls that take values in an unbounded set of measurable maps. This has non trivial impacts on the formulation and derivation of the associated partial differential equations.

1 :	CEntre de REcherches en MAthématiques de la DEcision (CEREMADE)
	CNRS : UMR7534 – Université Paris IX - Paris Dauphine

Domaine

:

Économie et finance quantitative/Finance quantitative Mathématiques/Equations aux dérivées partielles Mathématiques/Optimisation et contrôle

Mots Clés : stochastic target problem – mixed diffusion process – discontinuous viscosity solutions – quantile hedging

hal-00515522, version 3

http://hal.archives-ouvertes.fr/hal-00515522

oai:hal.archives-ouvertes.fr:hal-00515522

Contributeur : Ludovic Moreau <>

Soumis le : Mercredi 17 Août 2011, 14:53:17

Dernière modification le : Mercredi 17 Août 2011, 15:02:55