Evolutionary Hierarchical Credibility

33 Pages Posted: 21 Dec 2016 Last revised: 27 Jan 2017

See all articles by Greg Taylor

Greg Taylor

UNSW Australia Business School, School of Risk & Actuarial Studies

Date Written: December 20, 2016

Abstract

The hierarchical credibility model was introduced, and extended, in the seventies and early eighties. It deals with the estimation of parameters that characterize the nodes of a tree structure.

That model is limited, however, by the fact that its parameters are assumed fixed over time. This causes the model’s parameter estimates to track the parameters poorly when the latter are subject to variation over time.

The present paper seeks to remove this limitation by assuming the parameters in question to follow a process akin to a random walk over time, producing an evolutionary hierarchical model. The specific form of the model is compatible with the use of the Kalman filter for parameter estimation and forecasting.

The application of the Kalman filter is conceptually straightforward, but the tree structure of the model parameters can be extensive, and some effort is required to retain organization of the updating algorithm. This is achieved by suitable manipulation of the graph associated with the tree. The graph matrix then appears in the matrix calculations inherent in the Kalman filter.

A numerical example is included to illustrate the application of the filter to the model.

Keywords: credibility, credibility matrix, evolutionary model, graph matrix, hierarchy, Kalman filter, tree graph

JEL Classification: C53, G22

Suggested Citation

Taylor, Greg, Evolutionary Hierarchical Credibility (December 20, 2016). UNSW Business School Research Paper No. 2016ACTL08. Available at SSRN: https://ssrn.com/abstract=2888146 or http://dx.doi.org/10.2139/ssrn.2888146

Greg Taylor (Contact Author)

UNSW Australia Business School, School of Risk & Actuarial Studies ( email )

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