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The Esscher premium principle in risk theory: A Bayesian sensitivity study. (English) Zbl 0944.62094

Summary: The Esscher premium calculation principle is applied to the non-compound collective model in a robust Bayesian context. We consider that uncertainty with regard to the prior distribution can be represented by the assumption that the unknown prior distribution belongs to a class of distributions \(\Gamma\) and examine the ranges of the Bayesian premium when the priors belong to such a class. The assessment of the influence of the prior is termed sensitivity analysis or robustness analysis.

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
62F15 Bayesian inference
91B30 Risk theory, insurance (MSC2010)
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