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Risk Measures And Capital Requirements For Processes

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  • Marco Frittelli
  • Giacomo Scandolo

Abstract

In this paper we propose a generalization of the concepts of convex and coherent risk measures to a multiperiod setting, in which payoffs are spread over different dates. To this end, a careful examination of the axiom of translation invariance and the related concept of capital requirement in the one‐period model is performed. These two issues are then suitably extended to the multiperiod case, in a way that makes their operative financial meaning clear. A characterization in terms of expected values is derived for this class of risk measures and some examples are presented.

Suggested Citation

  • Marco Frittelli & Giacomo Scandolo, 2006. "Risk Measures And Capital Requirements For Processes," Mathematical Finance, Wiley Blackwell, vol. 16(4), pages 589-612, October.
    • Handle: RePEc:bla:mathfi:v:16:y:2006:i:4:p:589-612
    DOI: 10.1111/j.1467-9965.2006.00285.x
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    File URL: https://doi.org/10.1111/j.1467-9965.2006.00285.x
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    References listed on IDEAS

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    1. Riedel, Frank, 2004. "Dynamic coherent risk measures," Stochastic Processes and their Applications, Elsevier, vol. 112(2), pages 185-200, August.
    2. Frittelli, Marco & Rosazza Gianin, Emanuela, 2002. "Putting order in risk measures," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1473-1486, July.
    3. Jeremy Staum, 2004. "Fundamental Theorems of Asset Pricing for Good Deal Bounds," Mathematical Finance, Wiley Blackwell, vol. 14(2), pages 141-161, April.
    4. Giacomo Scandolo, 2004. "Models of Capital Requirements in Static and Dynamic Settings," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 33(3), pages 415-435, November.
    5. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    6. Barrieu, Pauline & El Karoui, Nicole, 2005. "Inf-convolution of risk measures and optimal risk transfer," LSE Research Online Documents on Economics 2829, London School of Economics and Political Science, LSE Library.
    7. Cheridito, Patrick & Delbaen, Freddy & Kupper, Michael, 2004. "Coherent and convex monetary risk measures for bounded càdlàg processes," Stochastic Processes and their Applications, Elsevier, vol. 112(1), pages 1-22, July.
    8. Patrick Cheridito & Freddy Delbaen & Michael Kupper, 2005. "Coherent and convex monetary risk measures for unbounded càdlàg processes," Finance and Stochastics, Springer, vol. 9(3), pages 369-387, July.
    9. Pauline Barrieu & Nicole El Karoui, 2005. "Inf-convolution of risk measures and optimal risk transfer," Finance and Stochastics, Springer, vol. 9(2), pages 269-298, April.
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