COMMON SHOCK MODELS FOR CLAIM ARRAYS
AuthorAvanzi, B; Taylor, G; Wong, B
Source TitleAstin Bulletin: The Journal of the ASTIN and AFIR Sections of the International Actuarial Association
PublisherCambridge University Press (CUP)
University of Melbourne Author/sAvanzi, Benjamin
Document TypeJournal Article
CitationsAvanzi, B., Taylor, G. & Wong, B. (2018). COMMON SHOCK MODELS FOR CLAIM ARRAYS. Astin Bulletin: The Journal of the ASTIN and AFIR Sections of the International Actuarial Association, 48 (3), pp.1109-1136. https://doi.org/10.1017/asb.2018.18.
Access StatusOpen Access
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.
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