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A Form Of Multivariate Pareto Distribution With Applications To Financial Risk Measurement

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  • Su, Jianxi
  • Furman, Edward

Abstract

A new multivariate distribution possessing arbitrarily parametrized and positively dependent univariate Pareto margins is introduced. Unlike the probability law of Asimit et al. (2010), the structure in this paper is absolutely continuous with respect to the corresponding Lebesgue measure. The distribution is of importance to actuaries through its connections to the popular frailty models, as well as because of the capacity to describe dependent heavy-tailed risks. The genesis of the new distribution is linked to a number of existing probability models, and useful characteristic results are proved. Expressions for, e.g., the decumulative distribution and probability density functions, (joint) moments and regressions are developed. The distributions of minima and maxima, as well as, some weighted risk measures are employed to exemplify possible applications of the distribution in insurance.

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  • Su, Jianxi & Furman, Edward, 2017. "A Form Of Multivariate Pareto Distribution With Applications To Financial Risk Measurement," ASTIN Bulletin, Cambridge University Press, vol. 47(1), pages 331-357, January.
    • Handle: RePEc:cup:astinb:v:47:y:2017:i:01:p:331-357_00
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    Citations

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    Cited by:

    1. Martín Egozcue & Jiang Wu & Ričardas Zitikis, 2017. "Optimal two-stage pricing strategies from the seller’s perspective under the uncertainty of buyer’s decisions," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-25, December.
    2. Ren Jiandong & Zitikis Ricardas, 2017. "CMPH: a multivariate phase-type aggregate loss distribution," Dependence Modeling, De Gruyter, vol. 5(1), pages 304-315, December.
    3. Gribkova, N.V. & Su, J. & Zitikis, R., 2022. "Inference for the tail conditional allocation: Large sample properties, insurance risk assessment, and compound sums of concomitants," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 199-222.
    4. 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.
    5. Su, Jianxi & Furman, Edward, 2017. "Multiple risk factor dependence structures: Distributional properties," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 56-68.
    6. Katarina Valaskova & Tomas Kliestik & Lucia Svabova & Peter Adamko, 2018. "Financial Risk Measurement and Prediction Modelling for Sustainable Development of Business Entities Using Regression Analysis," Sustainability, MDPI, vol. 10(7), pages 1-15, June.
    7. Furman, Edward & Kye, Yisub & Su, Jianxi, 2021. "Multiplicative background risk models: Setting a course for the idiosyncratic risk factors distributed phase-type," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 153-167.
    8. Övgücan Karadağ Erdemir, 2023. "A Comparative Perspective on Multivariate Modeling of Insurance Compensation Payments with Regression-Based and Copula-Based Models," EKOIST Journal of Econometrics and Statistics, Istanbul University, Faculty of Economics, vol. 0(39), pages 161-171, December.
    9. Su, Jianxi & Furman, Edward, 2017. "Multiple risk factor dependence structures: Copulas and related properties," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 109-121.

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