Evolutionary hierarchical credibility

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<title>Evolutionary hierarchical credibility</title>
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<abstract displayLabel="Summary">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 theKalman filter for parameter estimation and forecasting. The application of theKalman 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.</abstract>
<note type="statement of responsibility">Greg Taylor</note>
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<topic>Matemática del seguro</topic>
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<topic>Credibilidad</topic>
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<topic>Métodos estadísticos</topic>
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<topic>Teoría de la credibilidad</topic>
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<title>Astin bulletin</title>
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<publisher>Belgium : ASTIN and AFIR Sections of the International Actuarial Association</publisher>
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<identifier type="issn">0515-0361</identifier>
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<text>01/01/2018 Volumen 48 Número 1 - enero 2018 , p. 339-374</text>
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