Advertisement

Reflected Backward Stochastic Differential Equation with Super-Linear Growth

  • Khaled Bahlali
  • El Hassan Essaky
  • Boubakeur Labed
Conference paper
  • 155 Downloads

Abstract

We deal with reflected backward stochastic differential equations (RBSDE) in a d-dimensional convex region with super-linear growth coefficient. We prove, in this setting, various existence and uniqueness results. This is done with an unbounded terminal data.

Keywords

Backward Stochastic Differential Equation 
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Bahlali K.: Backward stochastic differential equations with locally Lipschitz coefficient, C. R. Acad. Sci. Paris Sér. I Math. 333 (2001) 481–486.MathSciNetzbMATHCrossRefGoogle Scholar
  2. [2]
    Bahlali K.: Existence and uniqueness of solutions for BSDEs with locally Lipschitz coefficient. Electron. Comm. Probab. 7 (2002) 169–179.Google Scholar
  3. [3]
    Bahlali K., Mezerdi B., Ouknine Y.: Some generic properties in backward stochastic differential equations with continuous coefficient, “Monte Carlo and probabilistic methods for partial differential equations (Monte Carlo, 2000)”.Google Scholar
  4. [4]
    Dermoune A., Hamadène S., Ouknine Y.: Backward stochastic differential equation with local time. Stochastics Stochastics Rep. 66 (1999) 103–119.MathSciNetzbMATHGoogle Scholar
  5. [5]
    El Karoui N., Peng S., Quenez M.-C.: Backward stochastic differential equations in finance. Math. Finance 7 (1997) 1–71.MathSciNetzbMATHCrossRefGoogle Scholar
  6. [6]
    El Karoui N., Kapoudjian C., Pardoux É., Peng S., Quenez M.-C.: Reflected solutions of backward SDE’s and related obstacle problems for PDE’s, Ann. Probab. 25 (1997) 702–737.MathSciNetzbMATHCrossRefGoogle Scholar
  7. [7]
    Gégout-Petit A., Pardoux E.: Équations différentielles stochastiques rétrogrades réfléchies dans un convexe, Stochastics Stochastics Rep. 57 (1996) 111–128.MathSciNetzbMATHGoogle Scholar
  8. [8]
    Hamadène S.: Multidimensional Backward SDE’s with uniformly continuous coefficients, Preprint Université du Maine 00–3, Le Mans 2000.Google Scholar
  9. [9]
    Hamadène S.: Équations différentielles stochastiques rétrogrades: le cas localement lipschitzien. Ann. Inst. H. Poincaré Probab. Statist. 32 (1996) 645–659.Google Scholar
  10. [10]
    Hamadène S., Lepeltier J.-P.: Zero-sum stochastic differential games and backward equations, Systems Control Lett. 24 (1995) 259–263.MathSciNetzbMATHCrossRefGoogle Scholar
  11. [11]
    Hamadène S., Ouknine Y.: Backward stochastic differential equations with jumps and random obstacle. To appear in Stochastics Stochastics Rep.Google Scholar
  12. [12]
    Lepeltier J.-P., San Martin J.: Backward stochastic differential equations with continuous coefficient, Statist. Probab. Lett. 32 (1997) 425–430.MathSciNetzbMATHCrossRefGoogle Scholar
  13. [13]
    Mao X.: Adapted solutions of backward stochastic differential equations with non-Lipschitz coefficients. Stochastic Process. Appl. 58 (1995) 281–292.MathSciNetzbMATHCrossRefGoogle Scholar
  14. [14]
    N’zi M.: Multivalued backward stochastic differential equations with local Lipschitz drift. Stochastics Stochastics Rep. 60 (1997) 205–218.MathSciNetzbMATHGoogle Scholar
  15. [15]
    N’zi M., Ouknine Y.: Multivalued backward stochastic differential equations with continuous coefficients. Random Oper. Stochastic Equations 5 (1997) 59–68.MathSciNetzbMATHGoogle Scholar
  16. [16]
    Ouknine Y.: Reflected backward stochastic differential equations with jumps, Stochastics Stochastics Rep. 65 (1998) 111–125.MathSciNetzbMATHGoogle Scholar
  17. [17]
    Pardoux É., Peng S.: Adapted solution of a backward stochastic differential equation. Systems Control Lett. 14 (1990) 55–61.MathSciNetzbMATHCrossRefGoogle Scholar
  18. [18]
    Pardoux É., Râ¸scanu A.: Backward stochastic differential equations with subdifferential operator and related variational inequalities. Stochastic Process. Appl. 76 (1998) 191–215.MathSciNetzbMATHCrossRefGoogle Scholar
  19. [19]
    Rong S.: On solutions of backward stochastic differential equations with jumps and applications. Stochastic Process. Appl. 66 (1997) 209–236.MathSciNetzbMATHCrossRefGoogle Scholar
  20. [20]
    Saisho Y.: Stochastic differential equations for multidimensional domain with reflecting boundary. Probab. Theory Related Fields 74 (1987) 455–477.MathSciNetzbMATHCrossRefGoogle Scholar
  21. [21]
    Tang S.J., Li X.J.: Necessary conditions for optimal control of stochastic systems with random jumps, SIAM J. Control Optim. 32 (1994) 1447–1475.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2004

Authors and Affiliations

  • Khaled Bahlali
    • 1
    • 2
  • El Hassan Essaky
    • 3
  • Boubakeur Labed
    • 4
  1. 1.UFR SciencesUVTLa Garde CedexFrance
  2. 2.CNRS LuminyCPTMarseille Cedex 9France
  3. 3.Département de MathématiquesUniversité Cadi Ayyad, Faculté des Sciences SemlaliaMarrakechMorocco
  4. 4.Département de MathématiquesUniversité Mohamed KhiderBiskraAlgérie

Personalised recommendations

Cite paper

Buy options