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

ISBN-10: 0470026774

ISBN-13: 9780470026779

There are quite a lot of variables for actuaries to think about whilst calculating a motorist’s coverage top class, similar to age, gender and sort of car. extra to those elements, motorists’ premiums are topic to event ranking platforms, together with credibility mechanisms and Bonus Malus structures (BMSs).

Actuarial Modelling of declare Counts provides a entire remedy of some of the adventure score structures and their relationships with possibility type. The authors summarize the newest advancements within the box, providing ratemaking platforms, 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 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 danger classification.
  • Presents credibility mechanisms as refinements of industrial BMSs.
  • Provides sensible functions with actual facts units processed with SAS software.

Actuarial Modelling of declare Counts is key examining for college kids in actuarial technological know-how, in addition to training and educational actuaries. it's also ideal for pros concerned about 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

Example text

7 Poisson Process Definition Recall that a stochastic process is a collection of random variables N t t ∈ indexed by a real-valued parameter t taking values in the index set . Usually, represents a set of observation times. In this book, we will be interested in continuous-time stochastic processes where = + . A stochastic process N t t ≥ 0 is said to be a counting process if t → N t is rightcontinuous and N t − N t− is 0 or 1. Intuitively speaking, N t represents the total number of events that have occurred up to time t.

In applied probability, the Inverse Gaussian distribution arises as the distribution of the first passage time to an absorbing barrier located at a unit distance from the origin in a Wiener process. 41) The probability mass function is given by Pr N = k = 0 exp − d d k!

Henceforth, we denote as F ·− the left limit of F , that is, F x− = lim F x = Pr X < x Suppose that X1 X2 Xn are n random variables defined on the same probability space Pr . Their marginal distribution functions F1 F2 Fn contain all the information about their associated probabilities. But how can the actuary encapsulate information about their properties relative to each other? As explained above, the key idea is to think of X1 X2 Xn T taking Xn as being components of a random vector X = X1 X2 n values in rather than being unrelated random variables each taking values in .

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Actuarial Modelling of Claim Counts: Risk Classification, Credibility and Bonus-Malus Systems by Michel Denuit, Xavier Marechal, Sandra Pitrebois, Jean-Francois Walhin


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