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On the Integrated Tail of the Deficit in the Renewal Risk Model

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  • Georgios Psarrakos

    (University of Piraeus)

Abstract

Let G(x, y) be the distribution of the deficit at the time of ruin in the renewal risk model. In this paper, we derive a geometric convolution representation for a function related to the integrated tail of the deficit. This integrated tail is a generalization of the stop loss-premium of the ruin probability, and the proposed convolution is a generalization of the equilibrium distribution of a compound geometric distribution (probability of non-ruin).

Suggested Citation

  • Georgios Psarrakos, 2015. "On the Integrated Tail of the Deficit in the Renewal Risk Model," Methodology and Computing in Applied Probability, Springer, vol. 17(2), pages 497-513, June.
    • Handle: RePEc:spr:metcap:v:17:y:2015:i:2:d:10.1007_s11009-013-9381-4
    DOI: 10.1007/s11009-013-9381-4
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    References listed on IDEAS

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    1. Psarrakos, Georgios, 2009. "A note on convolutions of compound geometric distributions," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1231-1237, May.
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