A note on existence and uniqueness for solutions of multidimensional reflected BSDEs

Jean François Chassagneux (Université d'Evry - Val d'Essonne)
Romuald Elie (Université Paris Dauphine)
Idris Kharroubi (Université Paris Dauphine)


In this note, we provide an innovative and simple approach for proving the existence of a unique solution for multidimensional reflected BSDEs associated to switching problems. Getting rid of a monotonicity assumption on the driver function, this approach simplifies and extends the recent results of Hu and Tang (2008) or Hamadene and Zhang (2010).

Full Text: Download PDF | View PDF online (requires PDF plugin)

Pages: 120-128

Publication Date: December 6, 2011

DOI: 10.1214/ECP.v16-1614


  1. N. El Karoui, C. Kapoudjan, E. Pardoux, S. Peng and M.C. Quenez. Reflected solutions of Backward SDE's and related obstacle problems for PDE's. The Annals of Probability 25 (1997), 702--737. Math. Review 1434123
  2. N. El Karoui, S. Peng and M.C. Quenez. Backward Stochastic Differential Equation in finance. Mathematical finance 7 (1997), 1--71. Math. Review 1434407
  3. S. Hamadene and J. Zhang. Switching problem and related system of reflected backward SDEs. Stochastic Processes and their Applications 120 (2010), 403--426. Math. Review 2594364
  4. Y. Hu and S. Tang. Multi-dimensional BSDE with oblique Reflection and optimal switching. Prob. Theory and Related Fields 147 (2008), 89--121. Math. Review 2594348
  5. S. Peng. Monotonic limit theory of BSDE and nonlinear decomposition theorem of Doob-Meyer's type. Prob. Theory and Related Fields 113 (1999), 473--499. Math. Review 1717527
  6. S. Peng and M. Xu. The smallest g-supermartingale and reflected BSDE with single and double L2 obstacles. Ann. I. H. Poincare 41 (2005), 605-630. Math. Review 2139035

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.