Two-sided bounds for the distribution of the deficit at ruin in the renewal risk model

We obtain lower and upper bounds for the severity of ruin in the renewal (Sparre Andersen) model of risk theory. We present two types of bounds: (i) bounds applicable generally; and (ii) exponential bounds for the case where the adjustment coefficient of the risk process exists. Many of these bounds...

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Bibliographic Details
Published in:Insurance, mathematics & economics mathematics & economics, 2007-07, Vol.41 (1), p.41-52
Main Authors: Chadjiconstantinidis, Stathis, Politis, Konstadinos
Format: Article
Language:English
Subjects:
Bankruptcy
Insurance
Mathematical methods
Modelling
Probability
Renewal equation
Renewal risk model
Renewals
Risk management
Risk theory
Ruin probability
Severity of ruin
Studies
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Summary:We obtain lower and upper bounds for the severity of ruin in the renewal (Sparre Andersen) model of risk theory. We present two types of bounds: (i) bounds applicable generally; and (ii) exponential bounds for the case where the adjustment coefficient of the risk process exists. Many of these bounds are obtained using existing bounds and the integral equation for the severity of ruin.
ISSN:0167-6687
1873-5959
DOI:10.1016/j.insmatheco.2006.09.001