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

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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.

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Authors and Affiliations

  1. Department of Mathematics, University of Osijek, Trg Ljudevita Gaja 6, Osijek, Croatia

    Danijel Grahovac

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  1. Danijel Grahovac
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Correspondence to Danijel Grahovac.

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Grahovac, D. Densities of Ruin-Related Quantities in the Cramér-Lundberg Model with Pareto Claims. Methodol Comput Appl Probab 20, 273–288 (2018). https://doi.org/10.1007/s11009-017-9551-x

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  • DOI: https://doi.org/10.1007/s11009-017-9551-x

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