Volume 24, 2020
|Page(s)||935 - 962|
|Published online||27 November 2020|
𝕃p solutions of reflected backward stochastic differential equations with jumps
Department of Mathematics, University of Pittsburgh,
PA 15260, USA.
* Corresponding author: firstname.lastname@example.org
Accepted: 18 September 2020
Given p ∈ (1, 2), we study 𝕃p-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 𝕃p solution via a fixed-point argument. The Y -component of the unique 𝕃p 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.
Mathematics Subject Classification: 60H10 / 60F25 / 60J76
Key words: Reflected backward stochastic differential equations with jumps / 𝕃p solutions / comparison theorem / optimal stopping / Snell envelope / Doob–Meyer decomposition / martingale representation theorem / fixed-point argument / g-evaluations
© EDP Sciences, SMAI 2020
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