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Modeling Severity and Measuring Tail Risk of Norwegian Fire Claims

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  • Vytaras Brazauskas
  • Andreas Kleefeld

Abstract

The probabilistic behavior of the claim severity variable plays a fundamental role in calculation of deductibles, layers, loss elimination ratios, effects of inflation, and other quantities arising in insurance. Among several alternatives for modeling severity, the parametric approach continues to maintain the leading position, which is primarily due to its parsimony and flexibility. In this article, several parametric families are employed to model severity of Norwegian fire claims for the years 1981 through 1992. The probability distributions we consider include generalized Pareto, lognormal-Pareto (two versions), Weibull-Pareto (two versions), and folded-t. Except for the generalized Pareto distribution, the other five models are fairly new proposals that recently appeared in the actuarial literature. We use the maximum likelihood procedure to fit the models and assess the quality of their fits using basic graphical tools (quantile-quantile plots), two goodness-of-fit statistics (Kolmogorov-Smirnov and Anderson-Darling), and two information criteria (AIC and BIC). In addition, we estimate the tail risk of “ground up” Norwegian fire claims using the value-at-risk and tail-conditional median measures. We monitor the tail risk levels over time, for the period 1981 to 1992, and analyze predictive performances of the six probability models. In particular, we compute the next-year probability for a few upper tail events using the fitted models and compare them with the actual probabilities.

Suggested Citation

  • Vytaras Brazauskas & Andreas Kleefeld, 2016. "Modeling Severity and Measuring Tail Risk of Norwegian Fire Claims," North American Actuarial Journal, Taylor & Francis Journals, vol. 20(1), pages 1-16, January.
  • Handle: RePEc:taf:uaajxx:v:20:y:2016:i:1:p:1-16
    DOI: 10.1080/10920277.2015.1062784
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    Cited by:

    1. repec:ibn:ijspnl:v:8:y:2019:i:4:p:1 is not listed on IDEAS
    2. Reynkens, Tom & Verbelen, Roel & Beirlant, Jan & Antonio, Katrien, 2017. "Modelling censored losses using splicing: A global fit strategy with mixed Erlang and extreme value distributions," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 65-77.
    3. Shi, Yue & Punzo, Antonio & Otneim, Håkon & Maruotti, Antonello, 2023. "Hidden semi-Markov models for rainfall-related insurance claims," Discussion Papers 2023/17, Norwegian School of Economics, Department of Business and Management Science.
    4. Ryan Martin, 2019. "Empirical Priors and Posterior Concentration Rates for a Monotone Density," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(2), pages 493-509, December.
    5. Queensley C Chukwudum, 2018. "Reinsurance Pricing of Large Motor Insurance Claims in Nigeria: An Extreme Value Analysis," Working Papers hal-01855973, HAL.
    6. 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.
    7. Nadezhda Gribkova & Ričardas Zitikis, 2019. "Weighted allocations, their concomitant-based estimators, and asymptotics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(4), pages 811-835, August.
    8. Queensley C. Chukwudum, 2019. "Reinsurance Pricing of Large Motor Insurance Claims in Nigeria: An Extreme Value Analysis," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 8(4), pages 1-12, July.
    9. Yuguang Fan & Philip S. Griffin & Ross Maller & Alexander Szimayer & Tiandong Wang, 2017. "The Effects of Largest Claim and Excess of Loss Reinsurance on a Company’s Ruin Time and Valuation," Risks, MDPI, vol. 5(1), pages 1-27, January.
    10. Punzo, Antonio & Bagnato, Luca & Maruotti, Antonello, 2018. "Compound unimodal distributions for insurance losses," Insurance: Mathematics and Economics, Elsevier, vol. 81(C), pages 95-107.
    11. Bowen Liu & Malwane M. A. Ananda, 2022. "A Generalized Family of Exponentiated Composite Distributions," Mathematics, MDPI, vol. 10(11), pages 1-18, June.

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