African Diaspora Journal of Mathematics

Reflected Generalized BSDEs with Random Time and Applications

A. Aman, A. Elouaflin, and M. N’Zi

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Abstract

In this paper, we aim to study solutions of reflected generalized BSDEs, involving the integral with respect to a continuous process, which is the local time of the diffusion on the boundary. We consider both a finite random terminal and a infinite horizon. In both case, we establish an existence and uniqueness result. As application, we give a characterization of an American pricing option in infinite horizon; and we also give a probabilistic formula for the viscosity solution of an obstacle problem for elliptic PDEs with a nonlinear Neumann boundary condition.

Article information

Source
Afr. Diaspora J. Math. (N.S.), Volume 14, Number 1 (2012), 83-105.

Dates
First available in Project Euclid: 18 July 2013

Permanent link to this document
https://projecteuclid.org/euclid.adjm/1374153558

Mathematical Reviews number (MathSciNet)
MR3080399

Zentralblatt MATH identifier
1279.60083

Subjects
Primary: 60H20, 60H30, 60H99

Keywords
American option pricing elliptic PDEs generalized backward stochastic differential equations Neumann boundary condition viscosity solution

Citation

Aman, A.; Elouaflin, A.; N’Zi, M. Reflected Generalized BSDEs with Random Time and Applications. Afr. Diaspora J. Math. (N.S.) 14 (2012), no. 1, 83--105. https://projecteuclid.org/euclid.adjm/1374153558


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