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On the Representation for Dynamically Consistent Nonlinear Evaluations: Uniformly Continuous Case

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  • Shiqiu Zheng

    (Beijing University of Technology
    North China University of Science and Technology)

  • Shoumei Li

    (Beijing University of Technology)

Abstract

A system of dynamically consistent nonlinear evaluation ( $${\mathcal {F}}$$ F -evaluation) provides an ideal characterization for the dynamical behaviors of risk measures and the pricing of contingent claims. The purpose of this paper is to study the representation for the $${\mathcal {F}}$$ F -evaluation by the solution of a backward stochastic differential equation (BSDE). Under a general domination condition, we prove that any $${\mathcal {F}}$$ F -evaluation can be represented by the solution of a BSDE with a generator which is Lipschitz in y and uniformly continuous in z.

Suggested Citation

  • Shiqiu Zheng & Shoumei Li, 2018. "On the Representation for Dynamically Consistent Nonlinear Evaluations: Uniformly Continuous Case," Journal of Theoretical Probability, Springer, vol. 31(1), pages 119-158, March.
    • Handle: RePEc:spr:jotpro:v:31:y:2018:i:1:d:10.1007_s10959-016-0705-5
    DOI: 10.1007/s10959-016-0705-5
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    References listed on IDEAS

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    1. Lepeltier, J. P. & San Martin, J., 1997. "Backward stochastic differential equations with continuous coefficient," Statistics & Probability Letters, Elsevier, vol. 32(4), pages 425-430, April.
    2. Cohen, Samuel N., 2012. "Representing filtration consistent nonlinear expectations as g-expectations in general probability spaces," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1601-1626.
    3. Royer, Manuela, 2006. "Backward stochastic differential equations with jumps and related non-linear expectations," Stochastic Processes and their Applications, Elsevier, vol. 116(10), pages 1358-1376, October.
    4. Jia, Guangyan, 2010. "Backward stochastic differential equations with a uniformly continuous generator and related g-expectation," Stochastic Processes and their Applications, Elsevier, vol. 120(11), pages 2241-2257, November.
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