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Optimal Numeraires for Risk Measures


  • Damir Filipovic

    (Department of Mathematics, University of Munich)


Can the usage of a risky numeraire with a greater than risk free expected return reduce the capital requirements in a solvency test? I will show that this is not the case. In fact, under a reasonable technical condition, there exists no optimal numeraire which yields smaller capital requirements than any other numeraire.

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  • Damir Filipovic, 2007. "Optimal Numeraires for Risk Measures," Research Paper Series 187, Quantitative Finance Research Centre, University of Technology, Sydney.
  • Handle: RePEc:uts:rpaper:187

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    1. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
    2. Filipovic, Damir & Kupper, Michael, 2007. "Monotone and cash-invariant convex functions and hulls," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 1-16, July.
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