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, similar to age, gender and sort of auto. extra to those elements, motorists’ charges are topic to event score platforms, together with credibility mechanisms and Bonus Malus platforms (BMSs).
Actuarial Modelling of declare Counts provides a entire remedy of a number of the event ranking structures and their relationships with threat type. The authors summarize the newest advancements within the box, providing ratemaking structures, while taking into consideration exogenous information.
- 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 platforms, and the combos 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 business BMSs.
- Provides functional purposes with genuine information units processed with SAS software.
Actuarial Modelling of declare Counts is vital studying for college students in actuarial technology, in addition to working towards and educational actuaries. it's also best for execs interested in the coverage undefined, utilized mathematicians, quantitative economists, monetary engineers and statisticians.
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Additional resources for Actuarial Modelling of Claim Counts: Risk Classification, Credibility and Bonus-Malus Systems
The mixing distribution described by F represents the heterogeneity of the portfolio of interest; dF is often called the structure function. 27) is an accident-proneness model: it assumes that a policyholder’s mean claim frequency does not change over time but allows some insured persons to have higher mean claim frequencies than others. 27). 1 Note that a better notation would have been oi F instead of oi since only the distribution function of matters to define the associated Poisson mixture.
Mixed Poisson Model for the Number of Claims The Poisson distribution often poorly fits observations made in a portfolio of policyholders. This is in fact due to the heterogeneity that is present in the portfolio: driving abilities vary from individual to individual. Therefore it is natural to multiply the mean frequency of the Poisson distribution by a positive random effect . 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.
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.