 On multivariate discounted compound renewal sums with time-dependent claims in the presence of reporting/payment delaysJae-Kyung Woo Insurance: Mathematics and Economics, 2016, vol. 70, issue C, 354-363 Abstract: In this paper, we consider an insurance portfolio containing several types of policies which may simultaneously face claims arising from the same catastrophe. A renewal counting process for the number of events causing claims and multivariate claim severities which are dependent on the occurrence time and/or the delay in reporting or payment are assumed. A unified model is proposed to study the time-dependent loss quantities such as the discounted aggregate reported/unreported claims and the number of the incurred but not reported (IBNR) claims. We then derive the joint moments of (i) different types of discounted aggregate claims until time t; and (ii) different types of discounted aggregate reported/unreported claims (including the total numbers of IBNR as special case) until time t. Finally, some numerical examples involving covariances and correlations of the aforementioned quantities are provided. Keywords: Multiline insurance; Renewal process; Multivariate distribution; Discounted aggregate claim costs; Reported/Unreported claims; IBNR claims; Joint moments; Covariance (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:70:y:2016:i:c:p:354-363 DOI: 10.1016/j.insmatheco.2016.07.004 Access Statistics for this article Insurance: Mathematics and Economics is currently edited by R. Kaas, Hansjoerg Albrecher, M. J. Goovaerts and E. S. W. Shiu More articles in Insurance: Mathematics and Economics from Elsevier |
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