Backward stochastic difference equations for dynamic convex risk measures on a binomial tree. (September 2015)

• Record Type: Journal Article
• Authors: Elliott, Robert J.; Siu, Tak Kuen; Cohen, Samuel N.
• Is Part Of: Journal of applied probability. Volume 52:Number 3(2015)
• Page Start: 771
• Page End: 785
• Publication Date: 2015-09
• Subjects: Dynamic convex risk measure, -- conditional nonlinear expectation, -- binomial tree, -- backward stochastic difference equation, -- stochastic distortion probability; 91G20, -- 91G80, -- 60H07; 519.2
• DOI: 10.1239/jap/1445543845
• Languages: English
• ISSNs: 0021-9002

Abstract

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.