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A note on the Swiss Solvency Test risk measure

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  • Filipovic, Damir
  • Vogelpoth, Nicolas

Abstract

In this paper we examine whether the Swiss Solvency Test risk measure is a coherent measure of risk as introduced in Artzner et al. [Artzner, P., Delbaen, F., Eber, J.M., Heath, D., 1999. Coherent measures of risk. Math. Finance 9, 203-228; Artzner, P., Delbaen, F., Eber, J.M., Heath, D., Ku, H., 2004. Coherent multiperiod risk adjusted values and Bellman's principle. Working Paper. ETH Zurich]. We provide a simple example which shows that it does not satisfy the axiom of monotonicity. We then find, as a monotonic alternative, the greatest coherent risk measure which is majorized by the Swiss Solvency Test risk measure.

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  • Filipovic, Damir & Vogelpoth, Nicolas, 2008. "A note on the Swiss Solvency Test risk measure," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 897-902, June.
    • Handle: RePEc:eee:insuma:v:42:y:2008:i:3:p:897-902
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    References listed on IDEAS

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    1. Denuit Michel & Dhaene Jan & Goovaerts Marc & Kaas Rob & Laeven Roger, 2006. "Risk measurement with equivalent utility principles," Statistics & Risk Modeling, De Gruyter, vol. 24(1), pages 1-25, July.
    2. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
    3. Denuit Michel & Dhaene Jan & Goovaerts Marc & Kaas Rob & Laeven Roger, 2006. "Risk measurement with equivalent utility principles," Statistics & Risk Modeling, De Gruyter, vol. 24(1), pages 1-25, July.
    4. 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.
    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.
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    Cited by:

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    2. Arai, Takuji & Asano, Takao & Nishide, Katsumasa, 2019. "Optimal initial capital induced by the optimized certainty equivalent," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 115-125.
    3. Eling, Martin & Pankoke, David, 2013. "Basis Risk, Procylicality, and Systemic Risk in the Solvency II Equity Risk Module," Working Papers on Finance 1306, University of St. Gallen, School of Finance.
    4. Balter, Anne G. & Pelsser, Antoon, 2020. "Pricing and hedging in incomplete markets with model uncertainty," European Journal of Operational Research, Elsevier, vol. 282(3), pages 911-925.

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