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

Georgios Psarrakos ()
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Georgios Psarrakos: University of Piraeus

Methodology and Computing in Applied Probability, 2015, vol. 17, issue 2, 497-513

Abstract: 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).

Keywords: Compound geometric distribution; Defective renewal equation; NWU (NBU); NWUC (NBUC); NWUE (NBUE); Ladder height; Ruin probability; Stop loss premium; Deficit at ruin; Primary 60K05; Secondary 91B30 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s11009-013-9381-4

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