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1 results

  • Backward stochastic difference equations for dynamic convex risk measures on a binomial tree

  • Part of
  • Robert J. Elliott, Tak Kuen Siu, Samuel N. Cohen
  • Journal:
    Journal of Applied Probability / Volume 52 / Issue 3 / September 2015
    Published online by Cambridge University Press:
    30 March 2016, pp. 771-785
    Print publication:
    September 2015
    • Article
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  • 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.