Description: In this paper, the Bayesian model of collective risk theory is extended in the sense that a large class of distributions is used instead of a single one. The authors then investigate the sensitivity of variance premium principle when the structure function belongs to that class. According to robust Bayesian methodology, the uncertainty in the prior can be modeled by specifying a class of priors instead of a single one. The authors examine the ranges of the Bayesian premium, also called experience rated premium, when the priors belong to that class. Most of the robust Bayesian procedures developed measures of sensitivity of quantities which can be expressed in terms of posterior expectation [e.g., mean, variance and probability of given sets]. Nevertheless, relatively few papers have been related to measure Bayesian sensitivity of quantities which can be expressed in terms of ratio of two posterior expectations, as occurs in the variance premium principle. Appropriate techniques to solve this situation are considered. Unimodality turns out to be very convenient for modelling subjective beliefs about the risk parameter. The very common Poisson-Gamma model is developed in depth using this paper's methodology.