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COMMON SHOCK MODELS FOR CLAIM ARRAYS

Published online by Cambridge University Press:  08 June 2018

Benjamin Avanzi ,
Greg Taylor  and
Bernard Wong
Benjamin Avanzi
Affiliation:
School of Risk and Actuarial Studies, UNSW Sydney Business School, UNSW Sydney, NSW 2052, Australia Département de Mathématiques et de Statistique, Université de Montréal, Montréal, Quebec H3T 1J4, Canada, E-Mail: [email protected]
Greg Taylor*
Affiliation:
School of Risk and Actuarial Studies, UNSW Sydney Business School, UNSW Sydney, NSW 2052, Australia
Bernard Wong
Affiliation:
School of Risk and Actuarial Studies, UNSW Sydney Business School, UNSW Sydney, NSW 2052, Australia, E-Mail: [email protected]
*
E-Mail: [email protected]
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Abstract

The paper is concerned with multiple claim arrays. In recognition of the extensive use by practitioners of large correlation matrices for the estimation of diversification benefits in capital modelling, we develop a methodology for the construction of such correlation structures (to any dimension). Indeed, the literature does not document any methodology by which practitioners, who often parameterise those correlations by means of informed guesswork, may do so in a disciplined and parsimonious manner.

We construct a broad and flexible family of models, where dependency is induced by common shock components. Models incorporate dependencies between observations both within arrays and between arrays. Arrays are of general shape (possibly with holes), but include the usual cases of claim triangles and trapezia that appear in the literature. General forms of dependency are considered with cell-, row-, column-, diagonal-wise, and other forms of dependency as special cases. Substantial effort is applied to practical interpretation of such matrices generated by the models constructed here.

Reasonably realistic examples are examined, in which an expression is obtained for the general entry in the correlation matrix in terms of a limited set of parameters, each of which has a straightforward intuitive meaning to the practitioner. This will maximise chance of obtaining a reliable matrix. This construction is illustrated by a numerical example.

Keywords

Claim arrayclaim dependencycommon shockcorrelationloss reservingG22C52C55
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 48 , Issue 3 , September 2018 , pp. 1109 - 1136
Copyright
Copyright © Astin Bulletin 2018 

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