Electronic Journal of Probability

Reflected Backward Stochastic Differential Equation with Jumps and Random Obstacle

Said Hamadène and Youssef Ouknine

Full-text: Open access

Abstract

In this paper we give a solution for the one-dimensional reflected backward stochastic differential equation when the noise is driven by a Brownian motion and an independent Poisson point process. We prove existence and uniqueness of the solution in using penalization and the Snell envelope theory. However both methods use a contraction in order to establish the result in the general case. Finally, we highlight the connection of such reflected BSDEs with integro-differential mixed stochastic optimal control.

Article information

Source
Electron. J. Probab., Volume 8 (2003), paper no. 2, 20 p.

Dates
First available in Project Euclid: 23 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464037575

Digital Object Identifier
doi:10.1214/EJP.v8-124

Mathematical Reviews number (MathSciNet)
MR1961164

Zentralblatt MATH identifier
1015.60051

Subjects
Primary: 60F10: Large deviations
Secondary: 60JH20 60H99: None of the above, but in this section

Keywords
Backward stochastic differential equation penalization Poisson point process martingale representation theorem integral-differential mixed control

Citation

Hamadène, Said; Ouknine, Youssef. Reflected Backward Stochastic Differential Equation with Jumps and Random Obstacle. Electron. J. Probab. 8 (2003), paper no. 2, 20 p. doi:10.1214/EJP.v8-124. https://projecteuclid.org/euclid.ejp/1464037575


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