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EVOLUTIONARY HIERARCHICAL CREDIBILITY

Published online by Cambridge University Press:  02 November 2017

Greg Taylor
Greg Taylor*
Affiliation:
UNSW Business School, Level 6, East Lobby, UNSW Business School Building E12, 2052 Sydney, Australia. Phone: +61 (0) 421 338 448.
*
E-Mail: [email protected]
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Abstract

The hierarchical credibility model was introduced, and extended, in the 70s and early 80s. 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. This 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

Credibilitycredibility matrixevolutionary modelgraph matrixhierarchyKalman filtertree graph
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 48 , Issue 1 , January 2018 , pp. 339 - 374
Copyright
Copyright © Astin Bulletin 2017 

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