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Credibility for Phase-type Distributions with a Single Risk Parameter
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When
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Monday 7th December at 5.15pm
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Where
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B617, Leverhulme Library, Columbia House
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Presentations
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Speaker
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David Stanford
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From
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University of Western Ontario
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Abstract
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Recently, interest has developed as to whether exact credibility results (wherein the optimal Bayesian credibility premium takes on a linear form) are applicable to phase-type distributions. This talk establishes that this is in general not the case, although it is true for special cases such as Erlang distributions. At the same time, by exploiting the fact that every phase-type distribution can be expressed as an infinite mixture of Erlang distributions of increasing order, we are able to establish that the optimal linear credibility premium can be calculated in a straightforward fashion. It is unclear at present as to whether the optimal Bayesian credibility premium can be calculated for any given phase-type distribution in a tractable manner, as we illustrate through a selection of examples.
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For further information
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Sabina Allam (Postgraduate Administrator) Ext. 6879
Department of Statistics, Columbia House
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