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Distortion Risk Measures or the Transformation of Unimodal Distributions into Multimodal Functions

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The particular subject of this paper, is to construct a general framework that can consider and analyse in the same time upside and downside risks. This paper offers a comparative analysis of concept risk measures, we focus on quantile based risk measure (ES and VaR), spectral risk measure and distortion risk measure. After introducing each measure, we investigate their interest and limit. Knowing that quantile based risk measure cannot capture correctly the risk aversion of risk manager and spectral risk measure can be inconsistent to risk aversion, we propose and develop a new distortion risk measure extending the work of Wang (2000) [38] and Sereda et al (2010) [34]. Finally, we provide a comprehensive analysis of the feasibility of this approach using the S&P500 data set from o1/01/1999 to 31/12/2011

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  • Dominique Guegan & Bertrand K Hassani, 2014. "Distortion Risk Measures or the Transformation of Unimodal Distributions into Multimodal Functions," Documents de travail du Centre d'Economie de la Sorbonne 14008, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    • Handle: RePEc:mse:cesdoc:14008
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    10. 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.
    11. Casper G. de Vries & Gennady Samorodnitsky & Bjørn N. Jorgensen & Sarma Mandira & Jon Danielsson, 2005. "Subadditivity Re–Examined: the Case for Value-at-Risk," FMG Discussion Papers dp549, Financial Markets Group.
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    16. Tsanakas, Andreas, 2004. "Dynamic capital allocation with distortion risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 223-243, October.
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    Cited by:

    1. Soren Bettels & Stefan Weber, 2024. "An Integrated Approach to Importance Sampling and Machine Learning for Efficient Monte Carlo Estimation of Distortion Risk Measures in Black Box Models," Papers 2408.02401, arXiv.org.
    2. Bertrand K. Hassani, 2014. "Risk Appetite in Practice: Vulgaris Mathematica," Post-Print halshs-01020293, HAL.
    3. Bertrand K Hassani, 2014. "Risk Appetite in Practice: Vulgaris Mathematica," Documents de travail du Centre d'Economie de la Sorbonne 14037, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    4. Bertrand K. Hassani, 2015. "Model Risk – From Epistemology to Management. Ipse se nihil scire id unum sciat. (Socrates' Plato)," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01163837, HAL.
    5. Bertrand K. Hassani, 2014. "Risk Appetite in Practice: Vulgaris Mathematica," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01020293, HAL.
    6. repec:hal:journl:halshs-01163837 is not listed on IDEAS
    7. Bertrand K Hassani, 2015. "Model Risk - From Epistemology to Management. Ipse se nihil scire id unum sciat. (Socrates' Plato)," Documents de travail du Centre d'Economie de la Sorbonne 15026, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.

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    More about this item

    Keywords

    Risk; VaR; distortion measures;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling

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