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Backward stochastic difference equations for dynamic convex risk measures on a binomial tree. (English) Zbl 1390.91333

Summary: 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.

MSC:

91G70 Statistical methods; risk measures
39A50 Stochastic difference equations
60H30 Applications of stochastic analysis (to PDEs, etc.)
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