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The Order-Statistic Claim Process With Dependent Claim Frequencies and Severities

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Abstract

Assuming that insurance claims arrive according to a general order-statistic (OS) point process, we explore ways for calculating the first two moments of the aggregate claim, thus facilitating the calculation of, and statistical inference for, quantities of actuarial interest such as the standard-deviation risk measure. We allow the OS process to govern claim sizes via claim arrival or, alternatively, claim interarrival times, which is a practically important feature. Given these general dependence structures and the underlying OS process, the herein obtained results extend and generalize a number of those in the literature.

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Authors and Affiliations

  1. Department of Statistical and Actuarial Sciences, University of Western Ontario, 1151 Richmond Street North, London, Ontario, N6A 5B7, Canada

    Kristina P. Sendova & Ričardas Zitikis

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  1. Kristina P. Sendova
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  2. Ričardas Zitikis
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Correspondence to Kristina P. Sendova.

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Sendova, K.P., Zitikis, R. The Order-Statistic Claim Process With Dependent Claim Frequencies and Severities. J Stat Theory Pract 6, 597–620 (2012). https://doi.org/10.1080/15598608.2012.719736

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  • DOI: https://doi.org/10.1080/15598608.2012.719736

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