COMPOSITION OF TIME-CONSISTENT DYNAMIC MONETARY RISK MEASURES IN DISCRETE TIME

Patrick Cheridito · Michael Kupper

147 citations0/0 files storedInternational Journal of Theoretical and Applied Finance

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Risk and Portfolio Optimization Stochastic processes and financial applications Probability and Risk Models

Abstract

In discrete time, every time-consistent dynamic monetary risk measure can be written as a composition of one-step risk measures. We exploit this structure to give new dual representation results for time-consistent convex monetary risk measures in terms of one-step penalty functions. We first study risk measures for random variables modelling financial positions at a fixed future time. Then we consider the more general case of risk measures that depend on stochastic processes describing the evolution of financial positions or cumulated cash flows. In both cases the new representations allow for a simple composition of one-step risk measures in the dual. We discuss several explicit examples and provide connections to the recently introduced class of dynamic variational preferences.

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References

1999Coherent Measures of Risk 1989Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: A Theoretical Framework 1989Maxmin expected utility with non-unique prior 1978Temporal Resolution of Uncertainty and Dynamic Choice Theory 1960Stationary Ordinal Utility and Impatience 2002Convex measures of risk and trading constraints 2002Stochastic Finance: An Introduction in Discrete Time 1992Stochastic Differential Utility

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