Analytical Expressions of Risks Involved in General Insurance

Let's, be the maximum value of si and t, the minimum value of the angular coefficient of the straight line connecting the point (si, Ai) with point (I, I), when i takes the values I, 2 ... n and the point (si, Ai) is taken to mean the vertex of the convex curve representing the generating function of the i (th), favorable risk. In a portfolio of m + n independent risks--where m are unfavorable and n favourable--Franckx finds that the superior limit of the probability that the aggregate amount of claims shall, not exceed k can be written " where I,,, is taken to mean the product of the generating functions for the m unfavorable risks."