Adding constraints to BSDEs with Jumps: an alternative to multidimensional reflections

2009/03/19 by Romuald Elie, Romuald Élie, Elie, Romuald +2
Decision Sciences · Economics, Econometrics and Finance · Engineering · Mathematics · #FOS: Mathematics #Probability (math.PR) #Risk and Portfolio Optimization #Stability and Control of Uncertain Systems #Stochastic processes and financial applications #math.PR

paper · pdf · doi:10.48550/arxiv.0903.3372

openalex publication_date 2009/03/19 · arxiv created 2011/03/09 · arxiv updated 2011/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is dedicated to the analysis of backward stochastic differential equations (BSDEs) with jumps, subject to an additional global constraint involving all the components of the solution. We study the existence and uniqueness of a minimal solution for these so-called constrained BSDEs with jumps via a penalization procedure. This new type of BSDE offers a nice and practical unifying framework to the notions of constrained BSDEs presented in [19] and BSDEs with constrained jumps introduced in [14]. More remarkably, the solution of a multidimensional Brownian reflected BSDE studied in [11] and [13] can also be represented via a well chosen one-dimensional constrained BSDE with jumps.This last result is very promising from a numerical point of view for the resolution of high dimensional optimal switching problems and more generally for systems of coupled variational inequalities

Related

• Backward stochastic viability property with jumps and applications to the comparison theorem for multidimensional BSDEs with jumps
• Reflected Backward SDEs with General Jumps
• Comparison theorems for multi-dimensional BSDEs with jumps and applications to constrained stochastic linear-quadratic control
• Reflected BSDEs with nonpositive jumps, and controller-and-stopper games
• Non-Markovian optimal stopping problems and constrained BSDEs with jump