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Bounds for Distorted Risk Measures

Author

Listed:
  • Goncalves Marcelo

    (Institute of Mathematics and Statistics, University of Sao Paulo, C.P. 66281, 05311-970 Sao Paulo, Brazil)

  • Kolev Nikolai

    (Institute of Mathematics and Statistics, University of Sao Paulo, C.P. 66281, 05311-970 Sao Paulo, Brazil. nkolev@ime.usp.br)

  • Fabris Antonio

    (Institute of Mathematics and Statistics, University of Sao Paulo, C.P. 66281, 05311-970 Sao Paulo, Brazil)

Abstract

The aim of this paper is to provide bounds for distorted risk measures when the joint distribution of the risk factors is unspecified but the marginal distributions are known. For convex distortion functions, a methodology to calculate the corresponding bounds is suggested and illustrated by several examples.

Suggested Citation

  • Goncalves Marcelo & Kolev Nikolai & Fabris Antonio, 2008. "Bounds for Distorted Risk Measures," Stochastics and Quality Control, De Gruyter, vol. 23(2), pages 243-255, January.
    • Handle: RePEc:bpj:ecqcon:v:23:y:2008:i:2:p:243-255:n:8
    DOI: 10.1515/EQC.2008.243
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    References listed on IDEAS

    as
    1. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    2. Embrechts, Paul & Puccetti, Giovanni, 2006. "Bounds for functions of multivariate risks," Journal of Multivariate Analysis, Elsevier, vol. 97(2), pages 526-547, February.
    3. Denneberg, Dieter, 1990. "Premium Calculation: Why Standard Deviation Should be Replaced by Absolute Deviation1," ASTIN Bulletin, Cambridge University Press, vol. 20(2), pages 181-190, November.
    4. Wang, Shaun, 1996. "Premium Calculation by Transforming the Layer Premium Density," ASTIN Bulletin, Cambridge University Press, vol. 26(1), pages 71-92, May.
    5. Paul Embrechts & Giovanni Puccetti, 2006. "Bounds for Functions of Dependent Risks," Finance and Stochastics, Springer, vol. 10(3), pages 341-352, September.
    Full references (including those not matched with items on IDEAS)

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