Skip to main content
SpringerLink
Log in
Book cover

Backward Stochastic Differential Equations pp 133–160Cite as

Reflected Backward SDEs

  • Chapter
  • First Online:

  • 4015 Accesses

Part of the book series: Probability Theory and Stochastic Modelling ((PTSM,volume 86))

Abstract

In this chapter we introduce (one-dimensional) reflected BSDEs, motivated by American option pricing. We shall establish its well-posedness, a priori estimates, as well as its connection with PDEs.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   54.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   69.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   99.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Cvitanic, J., Karatzas, I.: Backward stochastic differential equations with reflection and Dynkin games. Ann. Probab. 24(4), 2024–2056 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  2. Cvitanic, J., Karatzas, I., Soner, H.M.: Backward stochastic differential equations with constraints on the gains-process. Ann. Probab. 26(4), 1522–1551 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  3. El Karoui, N., Kapoudjian, C., Pardoux, E., Peng, S., Quenez, M.C.: Reflected solutions of backward SDE’s, and related obstacle problems for PDE’s. Ann. Probab. 25(2), 702–737 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  4. El Karoui, N., Peng, S., Quenez, M.C.: Backward stochastic differential equations in finance. Math. Financ. 7(1), 1–71 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  5. Hamadene, S.: Reflected BSDE’s with discontinuous barrier and application. Stoch. Stoch. Rep. 74(3–4), 571–596 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  6. Hamadene, S., Hassani, M.: BSDEs with two reflecting barriers: the general result. Probab. Theory Relat. Fields 132(2), 237–264 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  7. Hamadene, S., Jeanblanc, M.: On the starting and stopping problem: application in reversible investments. Math. Oper. Res. 32(1), 182–192 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  8. Hamadene, S., Zhang, J.: Switching problem and related system of reflected backward SDEs. Stoch. Process. Appl. 120(4), 403–426 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  9. Hu, Y., Tang, S.: Multi-dimensional BSDE with oblique reflection and optimal switching. Probab. Theory Relat. Fields 147(1–2), 89–121 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  10. Karatzas, I., Shreve, S.E.: Methods of Mathematical Finance. Applications of Mathematics (New York), vol. 39, xvi + 407 pp. Springer, New York (1998)

    Google Scholar 

  11. Ma, J., Zhang, J.: Representations and regularities for solutions to BSDEs with reflections. Stoch. Process. Appl. 115(4), 539–569 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  12. Peng, S.: Monotonic limit theorem of BSDE and nonlinear decomposition theorem of Doob-Meyer’s type. Probab. Theory Relat. Fields 113(4), 473–499 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  13. Peng, S., Xu, M.: The smallest g-supermartingale and reflected BSDE with single and double L 2 obstacles. Ann. Inst. H. Poincare Probab. Stat. 41(3), 605–630 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  14. Peng, S., Xu, M.: Reflected BSDE with a constraint and its applications in an incomplete market. Bernoulli 16(3), 614–640 (2010)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Southern California, Los Angeles, CA, USA

    Jianfeng Zhang

Authors
  1. Jianfeng Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer Science+Business Media LLC

About this chapter

Cite this chapter

Zhang, J. (2017). Reflected Backward SDEs. In: Backward Stochastic Differential Equations. Probability Theory and Stochastic Modelling, vol 86. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-7256-2_6

Download citation

Publish with us

Policies and ethics

Search

Navigation