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

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

There are quite a lot of variables for actuaries to contemplate while calculating a motorist’s assurance top rate, resembling age, gender and sort of auto. extra to those elements, motorists’ premiums are topic to adventure score structures, together with credibility mechanisms and Bonus Malus platforms (BMSs).

Actuarial Modelling of declare Counts provides a accomplished remedy of a few of the adventure score structures and their relationships with chance 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, useful method of a priori and a posteriori ratemaking in motor insurance.
  • Discusses the problems of declare frequency and declare severity, multi-event structures, and the mixtures of deductibles and BMSs.
  • Introduces contemporary advancements in actuarial technology and exploits the generalised linear version and generalised linear combined version to accomplish danger classification.
  • Presents credibility mechanisms as refinements of industrial BMSs.
  • Provides useful purposes with actual facts units processed with SAS software.

Actuarial Modelling of declare Counts is key analyzing for college kids in actuarial technology, in addition to practising and educational actuaries. it's also ideal for pros occupied with the assurance undefined, utilized mathematicians, quantitative economists, monetary engineers and statisticians.

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

Sample text

The larger the likelihood, the better the model. Maximum likelihood estimates have several desirable asymptotic properties: consistency, efficiency, asymptotic Normality, and invariance. The advantages of maximum likelihood estimation are that it fully uses all the information about the parameters contained in the data and that it is highly flexible. Most applied maximum likelihood problems lack closed-form solutions and so rely on numerical maximization of the likelihood function. The advent of fast computers has made this a minor issue in most cases.

A classic example in physics is the number of radioactive particles recorded by a Geiger counter in a fixed time interval. This property of the Poisson distribution means that it can act as a reference standard when deviations from pure randomness are suspected. Although the Poisson distribution is often called the law of small numbers, there is no need Actuarial Modelling of Claim Counts 16 for = nq to be small. It is the largeness of n and the smallness of q = /n that are important. However most of the data sets analysed in the literature show a small frequency.

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).

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