Given p ∈ (1, 2), we study 𝕃$$-solutions of a reflected backward stochastic differential equation with jumps (RBSDEJ) whose generator g is Lipschitz continuous in (y, z, u). Based on a general comparison theorem as well as the optimal stopping theory for uniformly integrable processes under jump filtration, we show that such a RBSDEJ with p-integrable parameters admits a unique 𝕃$$ solution via a fixed-point argument. The Y -component of the unique 𝕃$$ solution can be viewed as the Snell envelope of the reflecting obstacle 𝔏 under g-evaluations, and the first time Y meets 𝔏 is an optimal stopping time for maximizing the g-evaluation of reward 𝔏.
Mots-clés : Reflected backward stochastic differential equations with jumps, 𝕃p solutions, comparison theorem, optimal stopping, Snell envelope, Doob–Meyer decomposition, martingale representation theorem, fixed-point argument, $$-evaluations
@article{PS_2020__24_1_935_0,
author = {Yao, Song},
title = {$\mathbb{L}^p$ solutions of reflected backward stochastic differential equations with jumps},
journal = {ESAIM: Probability and Statistics},
pages = {935--962},
publisher = {EDP-Sciences},
volume = {24},
year = {2020},
doi = {10.1051/ps/2020026},
mrnumber = {4178791},
zbl = {1454.60084},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ps/2020026/}
}
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AU - Yao, Song
TI - $\mathbb{L}^p$ solutions of reflected backward stochastic differential equations with jumps
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PY - 2020
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EP - 962
VL - 24
PB - EDP-Sciences
UR - http://archive.numdam.org/articles/10.1051/ps/2020026/
DO - 10.1051/ps/2020026
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Yao, Song. $\mathbb{L}^p$ solutions of reflected backward stochastic differential equations with jumps. ESAIM: Probability and Statistics, Tome 24 (2020), pp. 935-962. doi : 10.1051/ps/2020026. http://archive.numdam.org/articles/10.1051/ps/2020026/
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