Actuarial Modelling of Claim Counts: Risk Classification, by Michel Denuit, Xavier Marechal, Sandra Pitrebois,

By Michel Denuit, Xavier Marechal, Sandra Pitrebois, Jean-Francois Walhin

There are a variety of variables for actuaries to contemplate whilst calculating a motorist’s coverage top class, akin to age, gender and kind of car. extra to those elements, motorists’ premiums are topic to adventure ranking structures, together with credibility mechanisms and Bonus Malus structures (BMSs).

Actuarial Modelling of declare Counts offers a entire remedy of a few of the adventure ranking structures and their relationships with possibility category. The authors summarize the latest advancements within the box, offering ratemaking structures, when making an allowance for exogenous information.

The text:

  • Offers the 1st self-contained, functional method of a priori and a posteriori ratemaking in motor insurance.
  • Discusses the problems of declare frequency and declare severity, multi-event platforms, and the combos of deductibles and BMSs.
  • Introduces fresh advancements in actuarial technological know-how and exploits the generalised linear version and generalised linear combined version to accomplish probability classification.
  • Presents credibility mechanisms as refinements of business BMSs.
  • Provides sensible functions with genuine info units processed with SAS software.

Actuarial Modelling of declare Counts is vital examining for college students in actuarial technological know-how, in addition to training and educational actuaries. it's also splendid for pros taken with the coverage undefined, utilized mathematicians, quantitative economists, monetary engineers and statisticians.

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Extra info for Actuarial Modelling of Claim Counts: Risk Classification, Credibility and Bonus-Malus Systems

Example text

The frequency will vary within the portfolio according to the nonobservable random variable . Obviously we will choose such that E = 1 because we want to obtain, on average, the frequency of the portfolio. Conditional on , we then have Pr N = k = =p k = exp − k k! 26) where p · is the Poisson probability mass function, with mean . The interpretation we give to this model is that not all policyholders in the portfolio have an identical frequency . Some of them have a higher frequency ( with ≥ 1), others have a lower frequency ( with ≤ 1).

Here, we discuss the Inverse Gaussian distribution. Inverse Gaussian Distribution The Inverse Gaussian distribution is an ideal candidate for modelling positive, right-skewed data. 39) . 40) For the last three decades, the Inverse Gaussian distribution has gained attention in describing and analyzing right-skewed data. The main appeal of Inverse Gaussian models lies in the fact that they can accommodate a variety of shapes, from highly skewed to almost Normal. Moreover, they share many elegant and convenient properties with Gaussian models.

Henceforth, we write N ∼ in n q to indicate that N is Binomially distributed, with size n and success probability q. Moments of the Binomial Distribution The mean of N ∼ in n q is n EN = k=1 n! qk 1 − q k−1 ! n−k ! 10) k=1 where M ∼ in n − 1 q . Furthermore, with M as defined before, n E N2 = k=1 n! kq k 1 − q k−1 ! n−k ! e. its variance is smaller than its mean : V N = nq 1 − q ≤ E N = nq. 8), raised to the nth power. This was expected since the Binomial random variable N can be seen as the Mixed Poisson Models for Claim Numbers 15 sum of n independent Bernoulli random variables with equal success probability q.

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