Representation and explicit calculation of Finite-time ruin probabilities

The paper presents in Section 3 and 4 two series expansions of U (w, t), the probability of non-ruin over a time-interval of length t when initial reserves are w. In Section 5 is developed a method for numerical approximation of U (w, t) given the first few moments of individual claim size distribution. This approximation is found to be very reliable for U (0, t) and fairly reliable in the range of (w, t) prodicing interesting values of U (w, t), even for quite eccentric claim size distributions. Numerical results are given in Section 5 and 6.