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

Patrick Cheridito and Michael Kupper
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Patrick Cheridito: ORFE, Princeton University, Princeton, NJ 08544, USA
Michael Kupper: Department of Mathematics, Humboldt University Berlin, 10099 Berlin, Germany

Chapter 7 in Finance at Fields, 2012, pp 181-206 from World Scientific Publishing Co. Pte. Ltd.

Abstract: AbstractIn 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.

Keywords: Mathematical Finance; Financial Mathematics; Risk Management; Asset Pricing; Computational Finance; Derivatives; Option Pricing; Portfolio Optimization (search for similar items in EconPapers)
Date: 2012
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