Integration of the normal power approximation

Gottfried Berger

ASTIN Bulletin, 1972, vol. 7, issue 1, 90-95

Abstract: Consider the set of functions Obviously, π1(x) represents the net premium of the excess cover over the priority x, and the variance thereof.If a distribution function F(x) = 1 − π0(x) is given, the set (1) can be generated by means of the recursion formulae Let us study the special class of d.fs. F(x) which satisfy where If these conditions are met, the integrals (1) have the solution: Aj(y) and Bj(y), respectively, are polynomials of rank jk and jk − 1. Their coefficients are determined by the equations: The system (5) is obtained by differentiation of (4) with respect to y, and observing (2).

Date: 1972
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