An Existence and Uniqueness Result for BSDEs with Uniformly Continuous Generators in z

Sheng Jun FAN, Long JIANG

Acta Mathematica Sinica, Chinese Series ›› 2011, Vol. 54 ›› Issue (2) : 187-194.

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Acta Mathematica Sinica, Chinese Series ›› 2011, Vol. 54 ›› Issue (2) : 187-194. DOI: 10.12386/A2011sxxb0020
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An Existence and Uniqueness Result for BSDEs with Uniformly Continuous Generators in z

  • Sheng Jun FAN, Long JIANG
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Abstract

This paper establishes an existence and uniqueness result for the solution to a one-dimensional backward stochastic differential equation (BSDE for short) whose generator satisfies Constantin’s condition in y and is uniformly continuous in z, which generalizes some known results.

 

Key words

backward stochastic differential equation / existence and uniqueness / uniformly continuous

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Sheng Jun FAN, Long JIANG. An Existence and Uniqueness Result for BSDEs with Uniformly Continuous Generators in z. Acta Mathematica Sinica, Chinese Series, 2011, 54(2): 187-194 https://doi.org/10.12386/A2011sxxb0020

References


[1] Pardoux E., Peng S., Adapted solution of a backward stochastic differential equation, Systems Control Letters, 1990, 14: 55-61.

[2] Mao X., Adapted solutions of backward stochastic differential equations with non-Lipschitz coefficients, Stochastic Process and Their Applications, 1995, 58: 281-292.

[3] Lepetier J. P., San Martin J., Backward stochastic differential equations with continuous coefficient, Statistics and Probability Letters, 1997, 32: 425-430.

[4] Pardoux E., BSDEs, weak convergence and homogenization of semilinear PDEs. Nonlinear Analysis, Differential Equations and Control (Montreal, QC,1998). Kluwer Academic Publishers, Dordrecht, 1999, 503-549.

[5] Kobylanski M., Backward stochastic differential equations and partial equations with quadratic growth, Ann. Probab., 2000, 28: 259-276.

[6] Constantin G., On the existence and uniqueness of adapted solutions for backward stochastic differential equations, Analele Universit?t?ii din Timi?soara, Seria Matematic?-Informatic?, 2001, XXXIX(2): 15-22.

[7] Briand Ph., Hu Y., Quadratic BSDEs with convex generators and unbounded terminal conditions, Probab. Theory Related Fields, 2008, 141: 543-567.

[8] Hamad`ene S., Multidimensional backward stochastic differential equations with uniformly continuous coefficients, Bernoulli, 2003, 9(3): 517-534.

[9] Jia G., A uniqueness theorem for the solution of backward stochastic differential equations, C.R. Acad. Sci. Paris, Ser. I, 2008, 346: 439-444.

[10] Fan S., Jiang L., Existence and uniqueness result for a BSDE whose generator is Lipschitz continuous in y and uniformly continuous in z, Journal of Applied Mathematics and Computing, 2010, doi: 10.1007/s12190- 010-0384-9.

[11] Fan S., Jiang L., Uniqueness result for BSDEs whose generator is monotonic in y and uniformly continuous in z, C.R. Acad. Sci. Paris, Ser. I, 2010, 348: 89-92.

[12] Cao Zh., Yan J., A comparison theorem for solutions of backward stochastic differential equations, Advances in Mathematics, 1999, 28(4): 304-308.

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