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UTILITY MAXIMIZATION WITH RANDOM HORIZON: A BSDE APPROACH

Monique Jeanblanc (), Thibaut Mastrolia (), Dylan Possamaï () and Anthony Réveillac ()
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Monique Jeanblanc: Université d’Évry-Val-d’Essonne, LaMME UMR CNRS 8071, IBGBI, 23 Boulevard de France, 91037 Evry Cedex, France
Thibaut Mastrolia: Université Paris Dauphine, CEREMADE UMR CNRS 7534, Place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France
Dylan Possamaï: Université Paris Dauphine, CEREMADE UMR CNRS 7534, Place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France
Anthony Réveillac: INSA, Département GMM, IMT UMR CNRS 5219, Université de Toulouse, 135 Avenue de Rangueil, F-31077 Toulouse Cedex 4, France

International Journal of Theoretical and Applied Finance (IJTAF), 2015, vol. 18, issue 07, 1-43

Abstract: In this paper, we study a utility maximization problem with random horizon and reduce it to the analysis of a specific backward stochastic differential equation (BSDE), which we call BSDE with singular coefficients, when the support of the default time is assumed to be bounded. We prove existence and uniqueness of the solution for the equation under interest. Our results are illustrated by numerical simulations.

Keywords: Quadratic BSDEs; enlargement of filtration; credit risk (search for similar items in EconPapers)
Date: 2015
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