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Auto-balanced common shock claim models

Published online by Cambridge University Press:  12 April 2023

Greg Taylor Open the ORCID record for Greg Taylor [Opens in a new window]  and
Phuong Anh Vu
Greg Taylor*
Affiliation:
School of Risk and Actuarial Studies, University of New South Wales, UNSW Sydney, NSW 2052, Australia
Phuong Anh Vu
Affiliation:
Taylor Fry, 45 Clarence Street, Sydney, NSW 2000, Australia
*
*Corresponding author. E-mail: greg_taylor60@hotmail.com
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Abstract

The paper is concerned with common shock models of claim triangles. These are usually constructed as linear combinations of shock components and idiosyncratic components. Previous literature has discussed the unbalanced property of such models, whereby the shocks may over- or under-contribute to some observations. The literature has also introduced corrections for this. The present paper discusses “auto-balanced” models, in which all shock and idiosyncratic components contribute to observations such that their proportionate contributions are constant from one observation to another. The conditions for auto-balance are found to be simple and applicable to a wide range of model structures. Numerical illustrations are given.

Keywords

Auto-balanceCommon shockLoss reservingMultivariate TweedieTweedie family of distributionsC02C51G22
Type
Original Research Paper
Information
Annals of Actuarial Science , Volume 17 , Issue 3 , November 2023 , pp. 580 - 605
Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Institute and Faculty of Actuaries

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