Interpretations of Semi-Parametric Mixture Models, Unbiased Estimators of Ultimate Value for Individual Claims and Conditional Probability Applications to Calculate Bulk Reserves

Semi-parametric mixture models have well documented technical advantages for modeling loss distributions. These technical advantages are documented in papers that focus on the estimation of the parameters of semi-parametric models. This paper assumes that the parameters have already been determined and then provides an interpretation of the results of the parameter estimation. This interpretation is intended to make semi-parametric models intuitively appealing. If we accept this interpretation of the parameters, then we can use conditional probability concepts to calculate bulk reserves either deterministically or in a stochastic framework.