Abstract
Based on a representation of the aggregate claims random variable as linear combination of counting random variables, a linear multivariate Bayesian model of risk theory is defined. In case of the classical risk theoretical assumptions, that is conditional Poisson likelihood counting variates and Gamma structural density, the model is shown to identify with a Bayesian version of the collective model of risk theory. An interesting multivariate credibility formula for the predictive mean is derived. A new type of recursive algorithm, called three-stage nested recursive scheme, allows to evaluate the predictive density and associated predictive stop-loss premiums in an effective way.
Reinsurance Research - Loss Distributions, Size of
Volume
23:1
Page
55-76
Year
1993
Categories
Business Areas
Reinsurance
Aggregate Excess/Stop Loss
Actuarial Applications and Methodologies
Ratemaking
Deductibles, Retentions, and Limits
Actuarial Applications and Methodologies
Ratemaking
Increased Limits
Financial and Statistical Methods
Loss Distributions
Publications
ASTIN Bulletin