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On ruin probability and aggregate claim representations for Pareto claim size distributions
Insurance: Mathematics and Economics
We generalize an integral representation for the ruin probability in a Cramer-Lundberg risk model with shifted (or also called US-)Pareto claim sizes, obtained by Ramsay (2003), to classical Pareto(a) claim size distributions with arbitrary real values a > 1 and derive its asymptotic expansion. Furthermore an integral representation for the tail of compound sums of Pareto-distributed claims is obtained and numerical illustrations of its performance in comparison to other aggregate claim approximations are provided.
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