Densities of Ruin-Related Quantities in the Cramér-Lundberg Model with Pareto Claims

Danijel Grahovac ()
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Danijel Grahovac: University of Osijek

Methodology and Computing in Applied Probability, 2018, vol. 20, issue 1, 273-288

Abstract: Abstract In this paper, we consider the classical yet widely applicable Cramér-Lundberg risk model with Pareto distributed claim sizes. Building on the previously known expression for the ruin probability we derive distributions of different ruin-related quantities. The results rely on the theory of scale functions and are intended to illustrate the simplicity and effectiveness of the theory. A particular emphasis is put on the tail behavior of the distributions of ruin-related quantities and their tail index value is established. Numerical illustrations are provided to show the influence of the claim sizes distribution tail index on the tails of the ruin-related quantities distribution.

Keywords: Cramér-Lundberg model; Pareto distribution; Scale function; Ruin-related quantities; Heavy-tailed distributions; 91B30; 60G51; 60G70 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s11009-017-9551-x

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