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Backward SDEs with two barriers and continuous coefficient: an existence result

Part of: Stochastic analysis

Published online by Cambridge University Press:  14 July 2016

Jean-Pierre Lepeltier  and
Jaime San Martín
Jean-Pierre Lepeltier*
Affiliation:
Université du Maine
Jaime San Martín*
Affiliation:
Universidad de Chile, Santiago
*
∗ Postal address: Laboratoire de Statistique et Processus, Université du Maine, 72085 Le Mans, Cedex 9, France. Email address: lepeltier@aviion.univ-lemans.fr
∗∗ Postal address: Departamento de Ingeniería Matemática, Centro de Modelamiento Matemático UMR 2071-CNRS, Universidad de Chile, Casilla 170-3, Correo 3, Santiago, Chile. Email address: jsanmart@dim.uchile.cl
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Abstract

In this work we prove the existence of a solution for a doubly reflected backward SDE with a continuous linearly increasing coefficient in the case where the barriers L and U are such that L < U on [0,T) and there exists a continuous semimartingale between L and U.

Keywords

Backward SDEbarrier

MSC classification

Primary: 60H20: Stochastic integral equations
Secondary: 60H30: Applications of stochastic analysis (to PDE, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 41 , Issue 1 , March 2004 , pp. 162 - 175
Copyright
Copyright © Applied Probability Trust 2004 

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References

Cvitanić, J., and Karatzas, I. (1996). Backward stochastic differential equations with reflection and Dynkin games. Ann. Prob. 24, 2024–2056.Google Scholar
Dellacherie, C., and Meyer, P.-A. (1975). Probabilités et Potentiel. Hermann, Paris.Google Scholar
El Karoui, N., Peng, S., and Quenez, M. C. (1997). Backward stochastic differential equations in finance. Math. Finance 7, 1–71.Google Scholar
ElKaroui, N. et al. (1997). Reflected solutions of backward SDEs, and related obstacle problems for PDEs. Ann. Prob. 25, 702–737.Google Scholar
Hamadene, S., Lepeltier, J.-P., and Matoussi, A. (1997). Double barrier backward SDEs with continuous coefficient. In Backward Stochastic Differential Equations (Pitman Res. Notes Math. Ser. 364), Longman, Harlow, pp. 161–175.Google Scholar
Lepeltier, J.-P. and San Martín, J. (1996). Backward SDEs with continuous coefficient. Statist. Prob. Lett. 14, 55–61.Google Scholar
Pardoux, E., and Peng, S. (1990). Adapted solution of a backward stochastic differential equation. System Control Lett. 14, 55–61.Google Scholar