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Interval Estimation of Actuarial Risk Measures

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  • Thomas Kaiser
  • Vytaras Brazauskas

Abstract

This article investigates performance of interval estimators of various actuarial risk measures. We consider the following risk measures: proportional hazards transform (PHT), Wang transform (WT), value-at-risk (VaR), and conditional tail expectation (CTE). Confidence intervals for these measures are constructed by applying nonparametric approaches (empirical and bootstrap), the strict parametric approach (based on the maximum likelihood estimators), and robust parametric procedures (based on trimmed means).Using Monte Carlo simulations, we compare the average lengths and proportions of coverage (of the true measure) of the intervals under two data-generating scenarios: “clean” data and “contaminated” data. In the “clean” case, data sets are generated by the following (similar shape) parametric families: exponential, Pareto, and lognormal. Parameters of these distributions are selected so that all three families are equally risky with respect to a fixed risk measure. In the “contaminated” case, the “clean” data sets from these distributions are mixed with a small fraction of unusual observations (outliers). It is found that approximate knowledge of the underlying distribution combined with a sufficiently robust estimator (designed for that distribution) yields intervals with satisfactory performance under both scenarios.

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  • Thomas Kaiser & Vytaras Brazauskas, 2006. "Interval Estimation of Actuarial Risk Measures," North American Actuarial Journal, Taylor & Francis Journals, vol. 10(4), pages 249-268.
  • Handle: RePEc:taf:uaajxx:v:10:y:2006:i:4:p:249-268
    DOI: 10.1080/10920277.2006.10597425
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    Cited by:

    1. Vytaras Brazauskas & Sahadeb Upretee, 2019. "Model Efficiency and Uncertainty in Quantile Estimation of Loss Severity Distributions," Risks, MDPI, vol. 7(2), pages 1-16, May.
    2. Ramsés H. Mena & Luis E. Nieto-Barajas, 2007. "Exchangeable Claims Sizes in a Compound Poisson Type Proces," ICER Working Papers - Applied Mathematics Series 19-2007, ICER - International Centre for Economic Research.
    3. Vytaras Brazauskas & Bruce L. Jones & Ricardas Zitikis, 2007. "Robustification and performance evaluation of empirical risk measures and other vector-valued estimators," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 175-199.

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