In this paper we consider BSDEs with Lipschitz coefficient reflected on two discontinuous (RCLL) barriers. In this case, we prove first the existence and uniqueness of the solution, then we also prove the convergence of the solutions of the penalized equations to the solution of the RBSDE. Since the method used in the case of continuous barriers (see Cvitanic and Karatzas, Ann. Probab. 24 (1996) 2024-2056 and Lepeltier and San Martín, J. Appl. Probab. 41 (2004) 162-175) does not work, we develop a new method, by considering the solutions of the penalized equations as the solutions of special RBSDEs and using some results of Peng and Xu in Annales of I.H.P. 41 (2005) 605-630.
Keywords: reflected backward stochastic differential equation, penalization method, optimal stopping, Snell envelope, Dynkin game
@article{PS_2007__11__3_0,
author = {Lepeltier, Jean-Pierre and Xu, Mingyu},
title = {Reflected backward stochastic differential equations with two {RCLL} barriers},
journal = {ESAIM: Probability and Statistics},
pages = {3--22},
publisher = {EDP Sciences},
volume = {11},
year = {2007},
doi = {10.1051/ps:2007002},
mrnumber = {2299643},
zbl = {1171.60352},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ps:2007002/}
}
TY - JOUR AU - Lepeltier, Jean-Pierre AU - Xu, Mingyu TI - Reflected backward stochastic differential equations with two RCLL barriers JO - ESAIM: Probability and Statistics PY - 2007 SP - 3 EP - 22 VL - 11 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/ps:2007002/ DO - 10.1051/ps:2007002 LA - en ID - PS_2007__11__3_0 ER -
%0 Journal Article %A Lepeltier, Jean-Pierre %A Xu, Mingyu %T Reflected backward stochastic differential equations with two RCLL barriers %J ESAIM: Probability and Statistics %D 2007 %P 3-22 %V 11 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/ps:2007002/ %R 10.1051/ps:2007002 %G en %F PS_2007__11__3_0
Lepeltier, Jean-Pierre; Xu, Mingyu. Reflected backward stochastic differential equations with two RCLL barriers. ESAIM: Probability and Statistics, Tome 11 (2007), pp. 3-22. doi : 10.1051/ps:2007002. https://www.numdam.org/articles/10.1051/ps:2007002/
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