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Mean-field backward stochastic differential equations with subdifferential operator and its applications

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  • Lu, Wen
  • Ren, Yong
  • Hu, Lanying

Abstract

In this paper, we deal with a class of mean-field backward stochastic differential equations with subdifferential operator corresponding to a lower semi-continuous convex function. By means of Yosida approximation, the existence and uniqueness of the solution is established. As an application, we give a probability interpretation for the viscosity solutions of a class of nonlocal parabolic variational inequalities.

Suggested Citation

  • Lu, Wen & Ren, Yong & Hu, Lanying, 2015. "Mean-field backward stochastic differential equations with subdifferential operator and its applications," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 73-81.
    • Handle: RePEc:eee:stapro:v:106:y:2015:i:c:p:73-81
    DOI: 10.1016/j.spl.2015.06.022
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    References listed on IDEAS

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    1. Maticiuc, Lucian & Rascanu, Aurel, 2010. "A stochastic approach to a multivalued Dirichlet-Neumann problem," Stochastic Processes and their Applications, Elsevier, vol. 120(6), pages 777-800, June.
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    3. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    4. Pardoux, Etienne & Rascanu, Aurel, 1998. "Backward stochastic differential equations with subdifferential operator and related variational inequalities," Stochastic Processes and their Applications, Elsevier, vol. 76(2), pages 191-215, August.
    5. Buckdahn, Rainer & Li, Juan & Peng, Shige, 2009. "Mean-field backward stochastic differential equations and related partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3133-3154, October.
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