Obliquely Reflected BSDEs

Chassagneux, Jean-François; Richou, Adrien

doi:10.48550/arxiv.1710.08989

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2020

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“…In this case, we obtain both existence and uniqueness for the solution of (1.1). Let us remark that our new results on Obliquely Reflected BSDEs allow us to treat some new optimal switching problems called "randomised switching problems" and introduced in the Section 5 of [2]. The main tool to obtain the existence result is to consider a sequence of penalised equation: for n P N, t P r0, T s,…”

Section: Introductionmentioning

confidence: 99%

Obliquely reflected backward stochastic differential equations

Chassagneux¹,

Richou²

2020

Ann. Inst. H. Poincaré Probab. Statist.

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In this paper, we study existence and uniqueness to multidimensional Reflected Backward Stochastic Differential Equations in an open convex domain, allowing for oblique directions of reflection. In a Markovian framework, combining a priori estimates for penalised equations and compactness arguments, we obtain existence results under quite weak assumptions on the driver of the BSDEs and the direction of reflection, which is allowed to depend on both Y and Z. In a non Markovian framework, we obtain existence and uniqueness result for direction of reflection depending on time and Y. We make use in this case of stability estimates that require some smoothness conditions on the domain and the direction of reflection.

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Section: Introductionmentioning

confidence: 99%