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September 2015 Backward stochastic difference equations for dynamic convex risk measures on a binomial tree
Robert J. Elliott, Tak Kuen Siu, Samuel N. Cohen
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J. Appl. Probab. 52(3): 771-785 (September 2015). DOI: 10.1239/jap/1445543845

Abstract

Using backward stochastic difference equations (BSDEs), this paper studies dynamic convex risk measures for risky positions in a simple discrete-time, binomial tree model. A relationship between BSDEs and dynamic convex risk measures is developed using nonlinear expectations. The time consistency of dynamic convex risk measures is discussed in the binomial tree framework. A relationship between prices and risks is also established. Two particular cases of dynamic convex risk measures, namely risk measures with stochastic distortions and entropic risk measures, and their mathematical properties are discussed.

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Robert J. Elliott. Tak Kuen Siu. Samuel N. Cohen. "Backward stochastic difference equations for dynamic convex risk measures on a binomial tree." J. Appl. Probab. 52 (3) 771 - 785, September 2015. https://doi.org/10.1239/jap/1445543845

Information

Published: September 2015
First available in Project Euclid: 22 October 2015

zbMATH: 06502535
MathSciNet: MR3414990
Digital Object Identifier: 10.1239/jap/1445543845

Subjects:
Primary: 91G20
Secondary: 60H07 , 91G80

Keywords: backward stochastic difference equation , binomial tree , conditional nonlinear expectation , Dynamic convex risk measure , stochastic distortion probability

Rights: Copyright © 2015 Applied Probability Trust

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Vol.52 • No. 3 • September 2015
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