$\mathbb{L}^p$ solutions of reflected backward stochastic differential equations with jumps

Yao, Song

doi:10.1051/ps/2020026

𝕃^{p}

solutions of reflected backward stochastic differential equations with jumps

Yao, Song

ESAIM: Probability and Statistics, Tome 24 (2020), pp. 935-962.

Suite au passage du modèle économique de la revue en S20, le texte intégral des articles des années 2019 et 2020 est accessible uniquement sur le site de l'éditeur et est réservé aux abonnés.

Résumé

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.

MR Zbl

DOI : 10.1051/ps/2020026

Classification : 60H10, 60F25, 60J76
Mots-clés : Reflected backward stochastic differential equations with jumps, 𝕃^p 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://www.numdam.org/articles/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://www.numdam.org/articles/10.1051/ps/2020026/

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