Backward Stochastic Differential Equations with Nonmarkovian Singular Terminal Values - Fédération de recherche Mathématiques des Pays de Loire Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2018

Backward Stochastic Differential Equations with Nonmarkovian Singular Terminal Values

Résumé

We solve a class of BSDE with a power function f(y) = y^q , q > 1, driving its drift and with the singular terminal boundary condition given by the indicator function of the ball B(m,r) or of its complement, where B(m, r) is the ball in the path space of continuous paths on [0,T] of the underlying Brownian motion centered at the constant function m and radius r. The solution involves the derivation and solution of a related heat equation in which f serves as a reaction term and which is accompanied by singular and discontinuous Dirichlet boundary conditions. Although the solution of the heat equation is discontinuous at the corners of the domain the BSDE has continuous sample paths with the prescribed terminal value.
Fichier principal
Vignette du fichier
revised_version.pdf (740.79 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-01401230 , version 1 (24-11-2016)
hal-01401230 , version 2 (15-01-2018)

Identifiants

  • HAL Id : hal-01401230 , version 2

Citer

Ali Devin Sezer, Thomas Kruse, Alexandre Popier, Ali Devin Sezer. Backward Stochastic Differential Equations with Nonmarkovian Singular Terminal Values. 2018. ⟨hal-01401230v2⟩
607 Consultations
191 Téléchargements

Partager

Gmail Facebook X LinkedIn More