Predictive stop-loss premiums and Studentʹs t-distribution

A Bayesian stop-loss prediction model is constructed from a mixture of a normal with a gamma conjugate prior. Its predictive density is a location-scale transformation of Studentʹs t-distribution. When no data are available for statistical prediction, the marginal distribution coincides with Bowersʹ distribution, introduced in Hürlimann (1993b), which generates the best stop-loss upper bounds by given mean, variance and range (− ∞, ∞) of a distribution. The present prediction model is justified using a conditional measure of safeness. Furthermore, it is shown how estimates of the approximation error made when replacing the predictive exact stop-loss premiums by a simple normal approximation can be obtained using computer simulations.