Utility maximization with random horizon: a BSDE approach

Monique Jeanblanc (1, 2) , Thibaut Mastrolia (3, 4) , Dylan Possamaï (4) , Anthony Réveillac (5, 6)

1 LaMME - Laboratoire de Mathématiques et Modélisation d'Evry
2 UEVE - Université d'Évry-Val-d'Essonne
3 Université Paris Dauphine-PSL
4 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
5 IMT - Institut de Mathématiques de Toulouse UMR5219
6 INSA Toulouse - Institut National des Sciences Appliquées - Toulouse

In this paper we study a utility maximization problem with random horizon and reduce it to the analysis of a specific 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.

Mots clés: credit risk AMS 2010 subject classification: Primary: 60H10; 60H20; 91G40; Secondary: 91B16; quadratic BSDEs; enlargement of filtration; 91G60; 93E20

Domaines: Probabilités [math.PR]

Monique Jeanblanc, Thibaut Mastrolia, Dylan Possamaï, Anthony Réveillac. Utility maximization with random horizon: a BSDE approach. International Journal of Theoretical and Applied Finance, 2015, 18 (7), pp.1550045. ⟨10.1142/S0219024915500454⟩. ⟨hal-01126684v3⟩