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

A system of dynamically consistent nonlinear evaluation ( 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 F -evaluation by the solution of a backward...

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Bibliographic Details
Published in:Journal of theoretical probability 2018-03, Vol.31 (1), p.119-158
Main Authors: Zheng, Shiqiu, Li, Shoumei
Format: Article
Language:English
Subjects:
Differential equations
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Representations
Statistics
Thermal analysis
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Summary:A system of dynamically consistent nonlinear evaluation ( 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 F -evaluation by the solution of a backward stochastic differential equation (BSDE). Under a general domination condition, we prove that any F -evaluation can be represented by the solution of a BSDE with a generator which is Lipschitz in y and uniformly continuous in z .
ISSN:0894-9840
1572-9230
DOI:10.1007/s10959-016-0705-5