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Estimating the Probability of a Rare Event via Elliptical Copulas

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  • Liang Peng

Abstract

A rare event happens with an extremely small probability but may cost billions of dollars. How to model and estimate the small probability of such an event is of importance to the insurance industry. Based on multivariate extreme value theory, methods have been proposed to extrapolate data into a far tail region. However, questions still remain open, such as the direction of extrapolation for a multivariate distribution and threshold selection for both marginals and the tail dependence function. In this paper we provide a way to estimate the probability of a rare event via modeling marginals and dependence by heavy tailed distributions and elliptical copulas, respectively. Hence, the direction of extrapolation becomes irrelevant. Moreover we employ recent threshold selection procedures to choose tuning parameters automatically.

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  • Liang Peng, 2008. "Estimating the Probability of a Rare Event via Elliptical Copulas," North American Actuarial Journal, Taylor & Francis Journals, vol. 12(2), pages 116-128.
    • Handle: RePEc:taf:uaajxx:v:12:y:2008:i:2:p:116-128
    DOI: 10.1080/10920277.2008.10597506
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    Cited by:

    1. Jean-François Quessy, 2021. "On nonparametric tests of multivariate meta-ellipticity," Statistical Papers, Springer, vol. 62(5), pages 2283-2310, October.
    2. Hashorva, Enkelejd, 2010. "On the residual dependence index of elliptical distributions," Statistics & Probability Letters, Elsevier, vol. 80(13-14), pages 1070-1078, July.
    3. Einmahl, John & Peng, Liang, 2024. "Variance-Reduced Risk Inference in Semi-Supervised Settings," Discussion Paper 2024-024, Tilburg University, Center for Economic Research.
    4. Einmahl, John & Peng, Liang, 2024. "Variance-Reduced Risk Inference in Semi-Supervised Settings," Other publications TiSEM 970231c1-c8e0-4f52-a0a4-f, Tilburg University, School of Economics and Management.
    5. Bücher Axel & Jaser Miriam & Min Aleksey, 2021. "Detecting departures from meta-ellipticity for multivariate stationary time series," Dependence Modeling, De Gruyter, vol. 9(1), pages 121-140, January.

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