Non-life insurance pricing with generalized linear models by Esbjörn Ohlsson, Björn Johansson

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By Esbjörn Ohlsson, Björn Johansson

Setting the cost of a non-life insurance plans consists of the statistical research of assurance info, considering quite a few homes of the insured item and the coverage holder. brought via British actuaries, generalized linear types (GLMs) have by way of now develop into a typical process used for pricing in lots of international locations. The e-book specializes in equipment in response to GLMs which were came upon priceless in actuarial perform. uncomplicated conception of GLMs in an assurance environment is gifted, with worthy extensions that aren't in universal use. The e-book can be utilized in actuarial schooling designed to satisfy the eu middle Syllabus and is written for actuarial scholars in addition to practising actuaries. To help the readers, it comprises case stories utilizing actual facts of a few complexity which are to be had at the www.

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They found that the estimates of this method were very close to those given by the MMT. This is consistent with our general experience that the choice of p in the Tweedie models is not that important for estimating relativities. 4 Modeling the Pure Premium In the end, it is the model for the pure premium that gives the tariff. One might consider using a Tweedie model with 1 < p < 2 to analyze the pure premium directly, as demonstrated by Jörgensen and Souza [JS94]. However, the standard GLM tariff analysis is to do separate analyses for claim frequency and claim severity, and then relativities for the pure premium are found by multiplying the results.

We summarize the results in the following lemma, returning to our usual notation with index i for the observation number. 1). Then the cumulant generating function exists and is given by Ψ (t) = b(θi + tφ/wi ) − b(θi ) , φ/wi and . , v(μi ) = b (b −1 (μi )). 4 Recall that in linear regression, we have a constant variance Var(Yi ) = φ, plus possibly a weight wi which we disregard for a moment. The most general assumption would be to allow Var(Yi ) = φi , but this would make the model heavily over-parameterized.

For the Poisson and gamma GLMs, we see that the deviance plays a similar role, and the figure indicates that the difference to a squared distance is not that large, if μ is close to y. g. the examples for the multiplicative normal, Poisson and gamma models in [IJ09]. 5. 1 Pearson’s Chi-Square and the Estimation of φ A classic measure of the goodness-of-fit of a statistical model is Pearson’s chisquare X 2 . In a generalized form for GLMs, this statistic is defined as1 X2 = i (yi − μˆ i )2 1 = Var(Yi ) φ wi i (yi − μˆ i )2 .

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