Insurance policy value and Pareto-optimal retention in the hypothesis of rare loss events

In the hypothesis of rare loss events, the general expression of the policy value has been determined as a functional of the “expected frequency / loss severity” function and of the retention function. Exponential disutility has been chosen after mathematical characterization of some of its economical aspects, where functional properties of quasiarithmetic averages have been used. By means of variational techniques, in the case of a risk neutral Insurer the Pareto-optimal retention function has been finally determined.