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Risk measures in ordered normed linear spaces with non-empty cone-interior

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  • Konstantinides, Dimitrios G.
  • Kountzakis, Christos E.
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    Abstract

    In this paper, we use tools from the theory of partially ordered normed linear spaces, especially the bases of cones. This work extends the well-known results for convex and coherent risk measures. Its linchpin consists in the replacement of the riskless bond by some interior point in the cone of the space of risks, which stands as the alternative numeraire.

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    Bibliographic Info

    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 48 (2011)
    Issue (Month): 1 (January)
    Pages: 111-122

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    Handle: RePEc:eee:insuma:v:48:y:2011:i:1:p:111-122

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    Web page: http://www.elsevier.com/locate/inca/505554

    Related research

    Keywords: Base of a cone Well-based cones Numeraire asset Coherent and convex risk measures Representability of risk measures;

    References

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    1. HERINGS, Jean-Jacques & POLEMARCHAKIS, Heracles, 1998. "Pareto improving price regulation when the asset market is incomplete," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 1998041, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Patrick Cheridito & Tianhui Li, 2009. "Risk Measures On Orlicz Hearts," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 19(2), pages 189-214.
    3. Stefan Jaschke & Uwe Küchler, 2001. "Coherent risk measures and good-deal bounds," Finance and Stochastics, Springer, Springer, vol. 5(2), pages 181-200.
    4. Frittelli, Marco & Rosazza Gianin, Emanuela, 2002. "Putting order in risk measures," Journal of Banking & Finance, Elsevier, Elsevier, vol. 26(7), pages 1473-1486, July.
    5. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 9(3), pages 203-228.
    6. Kreps, David M., 1981. "Arbitrage and equilibrium in economies with infinitely many commodities," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 8(1), pages 15-35, March.
    7. Stoica, George, 2006. "Relevant coherent measures of risk," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 42(6), pages 794-806, September.
    8. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, Springer, vol. 6(4), pages 429-447.
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    Cited by:
    1. Farkas, Walter & Koch-Medina, Pablo & Munari, Cosimo, 2014. "Capital requirements with defaultable securities," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 55(C), pages 58-67.

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