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A form of multivariate Pareto distribution with applications to financial risk measurement

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  • Jianxi Su
  • Edward Furman

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) [Asimit, V., Furman, E. and Vernic, R. (2010) On a multivariate Pareto distribution. Insurance: Mathematics and Economics 46(2), 308-316], 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.

Suggested Citation

  • Jianxi Su & Edward Furman, 2016. "A form of multivariate Pareto distribution with applications to financial risk measurement," Papers 1607.04737, arXiv.org.
    • Handle: RePEc:arx:papers:1607.04737
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    References listed on IDEAS

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    Cited by:

    1. Jianxi Su & Edward Furman, 2016. "Multiple risk factor dependence structures: Copulas and related properties," Papers 1610.02126, arXiv.org.
    2. Kazi Wahadul Hasan & Maliha Binte Hanif, 2022. "A pricing model for real-estate business in Bangladesh incorporating the uncertainty in buyer’s readiness: considerations during COVID-19 pandemic," SN Business & Economics, Springer, vol. 2(10), pages 1-16, October.
    3. Zhou, Ming & Dhaene, Jan & Yao, Jing, 2018. "An approximation method for risk aggregations and capital allocation rules based on additive risk factor models," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 92-100.
    4. Jianxi Su & Edward Furman, 2016. "Multiple risk factor dependence structures: Distributional properties," Papers 1607.04739, arXiv.org.

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