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

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  • Danijel Grahovac

    (University of Osijek)

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.

Suggested Citation

  • Danijel Grahovac, 2018. "Densities of Ruin-Related Quantities in the Cramér-Lundberg Model with Pareto Claims," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 273-288, March.
    • Handle: RePEc:spr:metcap:v:20:y:2018:i:1:d:10.1007_s11009-017-9551-x
    DOI: 10.1007/s11009-017-9551-x
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    References listed on IDEAS

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