This paper was inspired by comments by H. L. Seal in a series of lectures given to the Actuaries Club in New York and by a paper of his recently published in the Swiss Actuarial Journal (Seal, 1972 ). In his lectures he showed that the probability U(w, t) that a risk reserve at every epoch τ, where o < τ ≤ t will be non negative when the initial risk reserve is w is related to , the probability that the aggregate claim outgo through epoch t does not exceed by the relationship
where η is the security loading and f(x, t) = (∂/∂x) F(x, t).
It is assumed that the d.f. F(x, t) is differentiable eith regard to x with a possible exception at the point x = o.
Using an extension of the “ballot theorem” in Chapter III of Feller (1968 ) he showed that and observed that if numerical values of F(x, t) were available values of U(w, t) could be computed.