By Michel Denuit, Xavier Marechal, Sandra Pitrebois, Jean-Francois Walhin
There are quite a lot of variables for actuaries to contemplate whilst calculating a motorist’s assurance top class, similar to age, gender and sort of auto. extra to those elements, motorists’ charges are topic to adventure ranking structures, together with credibility mechanisms and Bonus Malus structures (BMSs).
Actuarial Modelling of declare Counts offers a complete therapy of a number of the adventure score structures and their relationships with possibility type. The authors summarize the newest advancements within the box, proposing ratemaking structures, while making an allowance for 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 structures, and the combos of deductibles and BMSs.
- Introduces contemporary advancements in actuarial technological know-how and exploits the generalised linear version and generalised linear combined version to accomplish possibility classification.
- Presents credibility mechanisms as refinements of industrial BMSs.
- Provides functional purposes with genuine facts units processed with SAS software.
Actuarial Modelling of declare Counts is key studying for college students in actuarial technological know-how, in addition to practising and educational actuaries. it's also excellent for execs all in favour of the assurance 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
The proportion of the portfolio in the different categories is q1 q2 q, respectively. Considering a given policyholder, the actuary does not know to which category he belongs, but the probability that he comes from category j is qj . The probability mass function of the number of claims reported by this insured driver is thus a weighted average of the probability mass functions associated with the k categories. 25) often leads to a dramatic increase in the number of parameters (the qj s and the j s).
This supports the fact that traffic accidents occur randomly in time. Assumption (iii) indicates that the probability that the policyholder files two or more Actuarial Modelling of Claim Counts 18 claims in a sufficiently small time interval is negligible when compared to the probability that he reports zero or only one claim. Link with the Poisson Distribution The Poisson process is intimately linked to the Poisson distribution, as precisely stated in the next result. 1 For any Poisson process, the number of events in any interval of length t is Poisson distributed with mean t, that is, for all s t ≥ 0, Pr N t + s − N s = n = exp − t tn n!
30) Therefore, unless is degenerated in 1, we observe that mixed Poisson distributions are overdispersed: the variance exceeds the mean. 31) . This = exp − dF 0 showing that mixed Poisson distributions have an excess of zeros compared to Poisson distributions with the same mean. This is in line with empirical studies, where actuaries often observe more policyholders producing 0 claims than the number predicted by the Poisson model. The following result that has been proved by Shaked (1980) reinforces this straightforward conclusion.