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Reflected Backward SDEs with Two Barriers Under Monotonicity and General Increasing Conditions

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Abstract

In this paper, we prove the existence and uniqueness result of the reflected BSDE with two continuous barriers under monotonicity and general increasing condition on y, with Lipschitz condition on z.

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References

  1. Alario Nazaret, M., Lepeltier, J.P., Marchal, B.: Dynkin games. In: Lecture Notes in Control and Information Sciences, vol. 43, pp. 23–42. Springer, Berlin (1982)

    Google Scholar 

  2. Bismut, J.M.: Sur un problème de Dynkin. Z. Wahrsch. Verw. Geb. 39, 31–53 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  3. Briand, Ph., Delyon, B., Hu, Y., Pardoux, E., Stoica, L.: L p solutions of BSDEs. Stoch. Process. Appl. 108, 109–129 (2003)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  7. Hamadène, S., Lepeltier, J.P., Matoussi, A.: Double barrier backward SDEs with continuous coefficient. In: El Karoui, N., Mazliak, L. (eds.), Backward Stochastic Differential Equations. Pitman Research Notes in Mathematics Series, vol. 364, pp. 161–177 (1997)

  8. Hamadène, S., Lepeltier, J.P., Peng, S.: BSDE with continuous coefficients and stochastic differential games. In: El Karoui, N., Mazliak, L. (eds.), Backward Stochastic Differential Equations. Pitman Research Notes in Mathematics Series, vol. 364, pp. 115–128 (1997)

  9. Lepeltier, J.P., Maingueneau, M.A.: Le jeu de Dynkin en théorie générale sans l’hypothèse de Mokoboski. Stochastics 13, 25–44 (1984)

    MATH  MathSciNet  Google Scholar 

  10. Lepeltier, J.P., Matoussi, A., Xu, M.: Reflected Backward stochastic differential equations under monotonicity and general increasing growth conditions. Adv. Appl. Probab. 37, 1–26 (2005)

    Article  MathSciNet  Google Scholar 

  11. Lepeltier, J.P., San Martín, J.: Backward SDE’s with two barriers and continuous coefficient. An existence result. J. Appl. Probab. 41, 162–175 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  12. Pardoux, E.: BSDE’s, weak convergence and homogenization of semilinear PDE’s. In: F.H., Clarke, R.J., Stern (eds.) Nonlinear Analysis, Differential Equations and Control, pp. 503–549. Kluwer Academic, Dordrecht (1999)

    Google Scholar 

  13. Pardoux, E., Peng, S.: Adapted solutions of backward stochastic differential equations. Syst. Control Lett. 14, 51–61 (1990)

    Article  MathSciNet  Google Scholar 

  14. Revuz, D., Yor, M.: Continuous Martingales and Brownian Motion. Springer, New York (1991)

    MATH  Google Scholar 

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Author notes

  1. Mingyu Xu

    Present address: Department of Financial Mathematics and Control Science, School of Mathematical Science, Fudan University, Shanghai, 200433, China

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  1. Departement des Mathématiques, Université du Maine, Le Mans, France

    Mingyu Xu

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  1. Mingyu Xu
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Correspondence to Mingyu Xu.

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Xu, M. Reflected Backward SDEs with Two Barriers Under Monotonicity and General Increasing Conditions. J Theor Probab 20, 1005–1039 (2007). https://doi.org/10.1007/s10959-007-0109-7

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  • DOI: https://doi.org/10.1007/s10959-007-0109-7

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