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Journal of Statistical Theory and Practice

, Volume 6, Issue 4, pp 597–620 | Cite as

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

Article

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.

Keywords

Claim process Aggregate claim Order-statistic point process OS point process Frequency distribution Severity distribution Risk measure Variance risk measure Standard-deviation risk measure 

AMS Subject Classification

62G30 62P05 60G55 

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Copyright information

© Grace Scientific Publishing 2012

Authors and Affiliations

  1. 1.Department of Statistical and Actuarial SciencesUniversity of Western OntarioLondonCanada

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