A Heavy-Tailed and Overdispersed Collective Risk Model

The collective risk model for the insurance claims is considered. The objective is to estimate a premium which is defined as a functional H specified up to an unknown parameter θ (the expected number of claims). Four principles of calculating a premium are applied. The Bayesian methodology, which combines the prior knowledge about a parameter θ with the knowledge in the form of a random sample is adopted. Two loss functions (the square-error loss function and the asymmetric loss function LINEX) are considered. Some uncertainty about a prior is assumed by introducing classes of priors. Considering one of the concepts of robust procedures the posterior regret Γ-minimax premiums are calculated, as an optimal robust premiums. A numerical example is presented.

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The Collective Risk Model

Fundamentals of Actuarial Mathematics ◽

10.1002/9781119971528.ch17 ◽

2011 ◽

pp. 259-290

Keyword(s):

Risk Model ◽

Collective Risk Model ◽

Collective Risk

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Practical applications of risk theory. Seminar, 29–30 September 1992

Journal of the Institute of Actuaries ◽

10.1017/s002026810003691x ◽

1993 ◽

Vol 120 (1) ◽

pp. 211-214

Author(s):

A. S. Macdonald

Keyword(s):

Case Studies ◽

Model Compound ◽

Risk Model ◽

Risk Theory ◽

Risk Models ◽

Compound Poisson ◽

Practical Applications ◽

Collective Risk Model ◽

Actuarial Mathematics ◽

Collective Risk

A seminar on ‘The Practical Applications of Risk Theory’ was held at Staple Inn on 29–30 September 1992, organised jointly by the Institute and the Department of Actuarial Mathematics and Statistics at Heriot-Watt University. The aim of the seminar was to combine introductory talks on several aspects of risk theory with detailed presentations of case studies by practitioners.The first three sessions dealt with risk models.Ms Mary Hardy gave a short survey of the classical collective risk model, compound Poisson distributions, and some simple approximations to such distributions.

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Poisson size-biased Lindley distribution and its applications

International Journal of Modeling Simulation and Scientific Computing ◽

10.1142/s1793962322500313 ◽

2021 ◽

Author(s):

Showkat Ahmad Dar ◽

Anwar Hassan ◽

Peer Bilal Ahmad

Keyword(s):

Parameter Estimation ◽

Count Data ◽

Hazard Rate ◽

Risk Model ◽

Probability Generating Function ◽

Likelihood Estimation ◽

Lindley Distribution ◽

Collective Risk Model ◽

Collective Risk ◽

Erlang Distributions

In this paper, a new model for count data is introduced by compounding the Poisson distribution with size-biased three-parameter Lindley distribution. Statistical properties, such as reliability, hazard rate, reverse hazard rate, Mills ratio, moments, shewness, kurtosis, moment genrating function, probability generating function and order statistics, have been discussed. Moreover, the collective risk model is discussed by considering the proposed distrubution as the primary distribution and the expoential and Erlang distributions as the secondary ones. Parameter estimation is done using maximum likelihood estimation (MLE). Finally a real dataset is discussed to demonstrate the suitability and applicability of the proposed distribution in modeling count dataset.

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An Appropriate Way to Switch from the Individual Risk Model to the Collective One

Astin Bulletin ◽

10.2143/ast.23.1.2005100 ◽

1993 ◽

Vol 23 (1) ◽

pp. 23-54 ◽

Cited By ~ 14

Author(s):

S. Kuon ◽

M. Radtke ◽

A. Reich

Keyword(s):

Risk Model ◽

Sufficient Conditions ◽

Approximation Error ◽

Individual Risk ◽

Risk Models ◽

Approximation Quality ◽

Collective Risk Model ◽

Collective Risk ◽

The Individual ◽

Necessary And Sufficient

AbstractFor some time now, the convenient and fast calculability of collective risk models using the Panjer-algorithm has been a well-known fact, and indeed practitioners almost always make use of collective risk models in their daily numerical computations. In doing so, a standard link has been preferred for relating such calculations to the underlying heterogeneous risk portfolio and to the approximation of the aggregate claims distribution function in the individual risk model. In this procedure until now, the approximation quality of the collective risk model upon which such calculations are based is unknown.It is proved that the approximation error which arises does not converge to zero if the risk portfolio in question continues to grow. Therefore, necessary and sufficient conditions are derived in order to obtain well-adjusted collective risk models which supply convergent approximations. Moreover, it is shown how in practical situations the previous natural link between the individual and the collective risk model can easily be modified to improve its calculation accuracy. A numerical example elucidates this.

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