PL EN


2005 | 14 | 11-25
Article title

Robust Bayesian estimation of insurance premium in collective risk model

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Selected contents from this journal
Title variants
Languages of publication
PL
Abstracts
EN
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 'theta' (the expected number of claims). Four principles of calculating a premium are applied: net, variance principle, Esscher and exponential. The Bayesian methodology, which combines the prior knowledge about a parameter 'theta' with the knowledge in the form of a random sample, is adopted. Two loss functions (the square loss function and the asymmetric loss function LINEX) are considered. The obtained Bayes premium depends on a choice of a prior. Some uncertainty about a prior is assumed by introducing four classes of priors. The oscillation of the Bayes estimator is calculated. Considering one of the concepts of robust procedures the posterior regret 'Gamma' -minimax premiums are calculated as optimal robust premiums. A numerical example is presented.
Year
Volume
14
Pages
11-25
Physical description
Document type
ARTICLE
Contributors
  • A. Boratynska, Szkola Gl√≥wna Handlowa w Warszawie, Instytut Ekonometrii, al Niepodleglosci 164, 02-554 Warszawa, Poland,
References
Document Type
Publication order reference
Identifiers
CEJSH db identifier
06PLAAAA00731800
YADDA identifier
bwmeta1.element.6c470cc1-84c9-3bb7-96eb-20b8351e342f
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