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Extreme risk measures for train delay time

Author

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  • Alfred Mbairadjim Moussa

    (LAMETA - Laboratoire Montpelliérain d'Économie Théorique et Appliquée - UM1 - Université Montpellier 1 - UPVM - Université Paul-Valéry - Montpellier 3 - INRA - Institut National de la Recherche Agronomique - Montpellier SupAgro - Centre international d'études supérieures en sciences agronomiques - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier)

  • Maïté Stéphan

    (LAMETA - Laboratoire Montpelliérain d'Économie Théorique et Appliquée - UM1 - Université Montpellier 1 - UPVM - Université Paul-Valéry - Montpellier 3 - INRA - Institut National de la Recherche Agronomique - Montpellier SupAgro - Centre international d'études supérieures en sciences agronomiques - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier)

Abstract

Following the financial literature on risk management, this paper introduces some risk measure for train delay time in the probabilistic framework. The measures of extreme risk are defined as quantile of train delay time assumed as positive continuous random variables. Their close-formed expressions and empirical calibration are discussed under the assumptions of log-normal, log-t-Student and Weibull distributions. A method for the performance evaluation of the proposed measure is presented. Finally, an empirical study illustrates the effectiveness of our modeling approach and shows the interest of its practical application.

Suggested Citation

  • Alfred Mbairadjim Moussa & Maïté Stéphan, 2014. "Extreme risk measures for train delay time," Post-Print hal-04910482, HAL.
    • Handle: RePEc:hal:journl:hal-04910482
    Note: View the original document on HAL open archive server: https://hal.science/hal-04910482v1
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    References listed on IDEAS

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    1. Börjesson, Maria & Eliasson, Jonas, 2011. "On the use of "average delay" as a measure of train reliability," Transportation Research Part A: Policy and Practice, Elsevier, vol. 45(3), pages 171-184, March.
    2. van Lint, J.W.C. & van Zuylen, Henk J. & Tu, H., 2008. "Travel time unreliability on freeways: Why measures based on variance tell only half the story," Transportation Research Part A: Policy and Practice, Elsevier, vol. 42(1), pages 258-277, January.
    3. 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.
    4. Engle, Robert F. & Manganelli, Simone, 2001. "Value at risk models in finance," Working Paper Series 75, European Central Bank.
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