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Type: Journal article
Title: Backward stochastic difference equations for dynamic convex risk measures on a binomial tree
Author: Elliott, R.
Siu, T.
Cohen, S.
Citation: Journal of Applied Probability, 2015; 52(3):771-785
Publisher: Applied Probability Trust
Issue Date: 2015
ISSN: 0021-9002
Statement of
Robert J. Elliott, Tak Kuen Siu, Samuel N. Cohen
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.
Keywords: Dynamic convex risk measure; conditional nonlinear expectation; binomial tree; backward stochastic difference equation; stochastic distortion probability
Rights: © Applied Probability Trust 2015
DOI: 10.1017/S0021900200113427
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Mathematical Sciences publications

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