Robust Bayesian estimation and prediction of reserves in exponential model with quadratic variance function. (English) Zbl 1395.62321
Summary: The exponential families with quadratic variance function, conjugate families of priors and square loss function is applied to the prediction of claim reserves. The robustness with respect to the priors is considered. The uncertainty of the prior information is modeled by two different classes of priors. The posterior regret \(\Gamma\)-minimax estimators and predictors are constructed.
MSC:
| 62P05 | Applications of statistics to actuarial sciences and financial mathematics |
| 62F15 | Bayesian inference |
| 62C10 | Bayesian problems; characterization of Bayes procedures |
| 62C20 | Minimax procedures in statistical decision theory |
| 91B30 | Risk theory, insurance (MSC2010) |
Keywords:
loss reserves; exponential model with quadratic variance function; classes of priors; \(\varepsilon\)-contamination; posterior regret \(\Gamma\)-minimax estimation and prediction; mean square error; chain ladder factorReferences:
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