
AbstractConsider 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 behaviour of these distributions as the initial capital tends to infinity are obtained. In particular, for positive safety loading the Cramer case, the case of subexponential distributions and some intermediate cases are discussed.
Applications of statistics to actuarial sciences and financial mathematics, Cramér condition, Gumbel distribution, Asymptotic distribution theory in statistics, Risk theory, insurance, generalized Pareto distribution, Ruin, asymptotic distribution, change of measure, Laplace transform, subexponential distribution, maximum domain of attraction
Applications of statistics to actuarial sciences and financial mathematics, Cramér condition, Gumbel distribution, Asymptotic distribution theory in statistics, Risk theory, insurance, generalized Pareto distribution, Ruin, asymptotic distribution, change of measure, Laplace transform, subexponential distribution, maximum domain of attraction
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