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

  • Robert J. Elliott (a1), Tak Kuen Siu (a2) and Samuel N. Cohen (a3)

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.

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Copyright

Corresponding author

Postal address: School of Mathematical Sciences, University of Adelaide, SA 5005, Australia. Email address: relliott@ucalgary.ca
∗∗ Postal address: Department of Applied Finance and Actuarial Studies, Faculty of Business and Economics, Macquarie University, Sydney, NSW 2109, Australia.
∗∗∗ Postal address: Mathematical Institute, University of Oxford, Andrew Wiles Building, Woodstock Road, Oxford OX2 6GG, UK.

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

  • Robert J. Elliott (a1), Tak Kuen Siu (a2) and Samuel N. Cohen (a3)

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