On The Distribution of the Surplus Prior to and at Ruin

Consider a classical compound Poisson model. The safety loading can be positive, negative or zero. Explicit expressions for the distributions of the surplus prior and at ruin are given in terms of the ruin probability. Moreover, the asymptotic behavior of these distributions as the initial capital tends to infinity are obtained. In particular, for positive safety loading the Cram6r case, the case of subexponential distributions and some intermediate cases are discussed. KEYWORDS Ruin, asymptotic distribution, change of measure, Laplace transform, subexponential distribution, Cramer condition, generalized Pareto distribution, maximum domain of attraction, Gumbel distribution