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Dynamic Risk Measures

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Advanced Mathematical Methods for Finance

Abstract

This paper gives an overview of the theory of dynamic convex risk measures for random variables in discrete-time setting. We summarize robust representation results of conditional convex risk measures, and we characterize various time consistency properties of dynamic risk measures in terms of acceptance sets, penalty functions, and by supermartingale properties of risk processes and penalty functions.

Financial support from the European Science Foundation (ESF) “Advanced Mathematical Methods for Finance” (AMaMeF) under the exchange grant 2281 and hospitality of Vienna University of Technology are gratefully acknowledged by B. Acciaio.

I. Penner was supported by the DFG Research Center Matheon “Mathematics for key technologies.” Financial support from the European Science Foundation (ESF) “Advanced Mathematical Methods for Finance” (AMaMeF) under the short visit grant 2854 is gratefully acknowledged.

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Author information

Authors and Affiliations

  1. Department of Economy, Finance and Statistics, University of Perugia, Via A. Pascoli 20, 06123, Perugia, Italy

    Beatrice Acciaio

  2. Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany

    Irina Penner

Authors
  1. Beatrice Acciaio
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  2. Irina Penner
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Correspondence to Beatrice Acciaio .

Editor information

Editors and Affiliations

  1. CMA, Department of Mathematics, University of Oslo, Oslo, 0316, Norway

    Giulia Di Nunno

  2. CMA, Department of Mathematics, University of Oslo, Oslo, 0316, Norway

    Bernt Øksendal

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Acciaio, B., Penner, I. (2011). Dynamic Risk Measures. In: Di Nunno, G., Øksendal, B. (eds) Advanced Mathematical Methods for Finance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18412-3_1

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