On the USP Calculation Under Solvency II and its Approximation with a Closed Form Formula

In this paper we recall and comment, aiming to help understanding, the model assumptions underlying the undertaking specific parameter (USP) method 1 as defined in the Solvency II regulation. In addition we propose an adjusted standard deviation estimator which also take into account the (estimated) portfolio volume of the solvency year under consideration.Moreover we present a closed-form formula for approximating the USP and provide some numerical examples based on real data showing the goodness of the approximation.This is a useful result for practicing actuaries since it allows to approximate the USP without performing any numerical optimization