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Risk measures with comonotonic subadditivity or convexity and respecting stochastic orders

  • Song, Yongsheng
  • Yan, Jia-An
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    This paper proposes some new classes of risk measures, which are not only comonotonic subadditive or convex, but also respect the (first) stochastic dominance or stop-loss order. We give their representations in terms of Choquet integrals w.r.t. distorted probabilities, and show that if the physical probability is atomless then a comonotonic subadditive (resp. convex) risk measure respecting stop-loss order is in fact a law-invariant coherent (resp. convex) risk measure.

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    File URL: http://www.sciencedirect.com/science/article/B6V8N-4XCYJ8X-1/2/4108eacbae75d73c4471e1fd5f189c66
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    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 45 (2009)
    Issue (Month): 3 (December)
    Pages: 459-465

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    Handle: RePEc:eee:insuma:v:45:y:2009:i:3:p:459-465
    Contact details of provider: Web page: http://www.elsevier.com/locate/inca/505554

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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. Touzi, Nizar & Schachermayer, Walter & Jouini, Elyès, 2006. "Law Invariant Risk Measures Have the Fatou Property," Economics Papers from University Paris Dauphine 123456789/342, Paris Dauphine University.
    3. Elyès Jouini & Walter Schachermayer & Nizar Touzi, 2006. "Law Invariant Risk Measures Have the Fatou Property," Post-Print halshs-00176522, HAL.
    4. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    5. Wang, Shaun S. & Young, Virginia R. & Panjer, Harry H., 1997. "Axiomatic characterization of insurance prices," Insurance: Mathematics and Economics, Elsevier, vol. 21(2), pages 173-183, November.
    6. Wang, Shaun & Dhaene, Jan, 1998. "Comonotonicity, correlation order and premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 22(3), pages 235-242, July.
    7. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
    8. L. Rüschendorf, 1983. "Solution of a statistical optimization problem by rearrangement methods," Metrika, Springer, vol. 30(1), pages 55-61, December.
    9. Frittelli, Marco & Rosazza Gianin, Emanuela, 2002. "Putting order in risk measures," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1473-1486, July.
    10. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
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