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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.

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.

Suggested Citation

  • Konstantinides, Dimitrios G. & Kountzakis, Christos E., 2011. "Risk measures in ordered normed linear spaces with non-empty cone-interior," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 111-122, January.
    • Handle: RePEc:eee:insuma:v:48:y:2011:i:1:p:111-122
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    References listed on IDEAS

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    1. P. Jean-Jacques Herings & Herakles Polemarchakis, 2006. "Pareto Improving Price Regulation when the Asset Market is Incomplete," Studies in Economic Theory, in: Christian Schultz & Karl Vind (ed.), Institutions, Equilibria and Efficiency, chapter 12, pages 225-244, Springer.
    2. Stoica, George, 2006. "Relevant coherent measures of risk," Journal of Mathematical Economics, Elsevier, vol. 42(6), pages 794-806, September.
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    7. 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.
    8. Patrick Cheridito & Tianhui Li, 2009. "Risk Measures On Orlicz Hearts," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 189-214, April.
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    Citations

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    Cited by:

    1. Walter Farkas & Pablo Koch-Medina & Cosimo Munari, 2014. "Beyond cash-additive risk measures: when changing the numéraire fails," Finance and Stochastics, Springer, vol. 18(1), pages 145-173, January.
    2. Christos E. Kountzakis & Damiano Rossello, 2019. "Acceptability Indices of Performance for Bounded C\`adl\`ag Processes," Papers 1911.02261, arXiv.org.
    3. Walter Farkas & Pablo Koch-Medina & Cosimo Munari, 2012. "Beyond cash-additive risk measures: when changing the num\'{e}raire fails," Papers 1206.0478, arXiv.org, revised Feb 2014.
    4. Jaunė, Eglė & Šiaulys, Jonas, 2022. "Asymptotic risk decomposition for regularly varying distributions with tail dependence," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    5. Farkas, Walter & Koch-Medina, Pablo & Munari, Cosimo, 2014. "Capital requirements with defaultable securities," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 58-67.
    6. Walter Farkas & Pablo Koch-Medina & Cosimo Munari, 2012. "Capital requirements with defaultable securities," Papers 1203.4610, arXiv.org, revised Jan 2014.
    7. W. Farkas & A. Smirnow, 2016. "Intrinsic risk measures," Papers 1610.08782, arXiv.org.

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