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

Robert J. Elliott*, Tak Kuen Siu, Samuel N. Cohen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)771-785
Number of pages15
JournalJournal of Applied Probability
Volume52
Issue number3
DOIs
Publication statusPublished - 1 Sep 2015

Keywords

  • Backward stochastic difference equation
  • Binomial tree
  • Conditional nonlinear expectation
  • Dynamic convex risk measure
  • Stochastic distortion probability

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