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Bayesian Analysis Of Insurance Losses Using The Buhlmann-Straub Credibility Model, Abraham J. Van Der Merwe, Kobus N. Bekker
Bayesian Analysis Of Insurance Losses Using The Buhlmann-Straub Credibility Model, Abraham J. Van Der Merwe, Kobus N. Bekker
Journal of Actuarial Practice (1993-2006)
We propose a Bayesian analysis to develop credibility estimates of the well known Biihlmann-Straub model. We describe simple numerical methods to obtain exact posterior distributions and predictive densities under this model. These distributions are obtained through Monte Carlo simulations that generate independent samples from the joint posterior distribution. Our methods are therefore preferable to methods such as Gibbs sampling, which generates dependent samples from the joint distribution. The methods discussed also can be extended to more complicated credibility models.
Linear Empirical Bayes Estimation Of Survival Probabilities With Partial Data, Mostafa Mashayekhi
Linear Empirical Bayes Estimation Of Survival Probabilities With Partial Data, Mostafa Mashayekhi
Journal of Actuarial Practice (1993-2006)
In this paper we consider linear empirical Bayes estimation of survival probabilities with partial data from right-censored and possibly left-truncated observations. Such data are produced by studies in which the exact times of death are not recorded and the length of time that each subject may be under observation cannot exceed one unit of time. We obtain asymptotically optimal linear empirical Bayes estimators, with respect to the squared error loss function, under the assumption that the probability of death under observation in a unit time interval is proportional to the length of observation. This assumption is sometimes implied by Balducci's …