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Reflected backward stochastic differential equations under monotonicity and general increasing growth conditions

Part of: Stochastic analysis Stochastic processes

Published online by Cambridge University Press:  01 July 2016

J.-P. Lepeltier ,
A. Matoussi  and
M. Xu
J.-P. Lepeltier*
Affiliation:
Université du Maine
A. Matoussi*
Affiliation:
Université du Maine
M. Xu*
Affiliation:
Université du Maine
*
∗ Postal address: Département de Mathématiques, Laboratoire de Statistique et processus, Université du Maine, Bp 535, 72085 Le Mans Cedex, France.
∗ Postal address: Département de Mathématiques, Laboratoire de Statistique et processus, Université du Maine, Bp 535, 72085 Le Mans Cedex, France.
∗ Postal address: Département de Mathématiques, Laboratoire de Statistique et processus, Université du Maine, Bp 535, 72085 Le Mans Cedex, France.
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Abstract

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We prove the existence and uniqueness of the solution to certain reflected backward stochastic differential equations (RBSDEs) with one continuous barrier and deterministic terminal time, under monotonicity, and general increasing growth conditions on the associated coefficient. As an application, we obtain, in some constraint cases, the price of an American contingent claim as the unique solution of such an RBSDE.

Keywords

Reflected backward stochastic differential equationmonotonicity conditiongeneral increasing growth conditionpenalization method

MSC classification

Primary: 60H10: Stochastic ordinary differential equations
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 37 , Issue 1 , March 2005 , pp. 134 - 159
Copyright
Copyright © Applied Probability Trust 2005 

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