Electronic Communications in Probability

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

Jean François Chassagneux, Romuald Elie, and Idris Kharroubi

Full-text: Open access

Abstract

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).

Article information

Source
Electron. Commun. Probab., Volume 16 (2011), paper no. 12, 120-128.

Dates
Accepted: 6 December 2011
First available in Project Euclid: 7 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465261968

Digital Object Identifier
doi:10.1214/ECP.v16-1614

Mathematical Reviews number (MathSciNet)
MR2775350

Zentralblatt MATH identifier
1232.93095

Subjects
Primary: 93E20: Optimal stochastic control
Secondary: 65C99: None of the above, but in this section 60H30: Applications of stochastic analysis (to PDE, etc.)

Keywords
BSDE with oblique reflections Switching problems

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Chassagneux, Jean François; Elie, Romuald; Kharroubi, Idris. A note on existence and uniqueness for solutions of multidimensional reflected BSDEs. Electron. Commun. Probab. 16 (2011), paper no. 12, 120--128. doi:10.1214/ECP.v16-1614. https://projecteuclid.org/euclid.ecp/1465261968


Export citation

References

  • 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.
  • N. El Karoui, S. Peng and M.C. Quenez. Backward Stochastic Differential Equation in finance. Mathematical finance 7 (1997), 1–71.
  • S. Hamadene and J. Zhang. Switching problem and related system of reflected backward SDEs. Stochastic Processes and their Applications 120 (2010), 403–426.
  • Y. Hu and S. Tang. Multi-dimensional BSDE with oblique Reflection and optimal switching. Prob. Theory and Related Fields 147 (2008), 89–121.
  • 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.
  • 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.