# Adding constraints to BSDEs with jumps: an alternative to multidimensional reflections

ESAIM: Probability and Statistics (2014)

- Volume: 18, page 233-250
- ISSN: 1292-8100

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topElie, Romuald, and Kharroubi, Idris. "Adding constraints to BSDEs with jumps: an alternative to multidimensional reflections." ESAIM: Probability and Statistics 18 (2014): 233-250. <http://eudml.org/doc/273641>.

@article{Elie2014,

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 [S. Peng and M. Xu, Preprint. (2007)] and BSDEs with constrained jumps introduced in [I. Kharroubi, J. Ma, H. Pham and J. Zhang, Ann. Probab. 38 (2008) 794–840]. More remarkably, the solution of a multidimensional Brownian reflected BSDE studied in [Y. Hu and S. Tang, Probab. Theory Relat. Fields 147 (2010) 89–121] and [S. Hamadène and J. Zhang, Stoch. Proc. Appl. 120 (2010) 403–426] 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.},

author = {Elie, Romuald, Kharroubi, Idris},

journal = {ESAIM: Probability and Statistics},

keywords = {stochastic control; switching problems; BSDE with jumps; reflected BSDE; backward stochastic differential equations (BSDEs) with jumps},

language = {eng},

pages = {233-250},

publisher = {EDP-Sciences},

title = {Adding constraints to BSDEs with jumps: an alternative to multidimensional reflections},

url = {http://eudml.org/doc/273641},

volume = {18},

year = {2014},

}

TY - JOUR

AU - Elie, Romuald

AU - Kharroubi, Idris

TI - Adding constraints to BSDEs with jumps: an alternative to multidimensional reflections

JO - ESAIM: Probability and Statistics

PY - 2014

PB - EDP-Sciences

VL - 18

SP - 233

EP - 250

AB - 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 [S. Peng and M. Xu, Preprint. (2007)] and BSDEs with constrained jumps introduced in [I. Kharroubi, J. Ma, H. Pham and J. Zhang, Ann. Probab. 38 (2008) 794–840]. More remarkably, the solution of a multidimensional Brownian reflected BSDE studied in [Y. Hu and S. Tang, Probab. Theory Relat. Fields 147 (2010) 89–121] and [S. Hamadène and J. Zhang, Stoch. Proc. Appl. 120 (2010) 403–426] 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.

LA - eng

KW - stochastic control; switching problems; BSDE with jumps; reflected BSDE; backward stochastic differential equations (BSDEs) with jumps

UR - http://eudml.org/doc/273641

ER -

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