Estimation of the Coefficient of Variation of the Excess of Loss By Means of Jensen's Inequality for Convex Functions. The Connection with the Theory of Life Times

This note deals with a way to determine upper and lower bounds for the coefficient of variation of the total claim costs in a year in excess of a certain limit value. In marry a publication attention has been paid to the question of calculating, in addition to the mean of the excess costs, the variance of these costs.