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Bounds for the Ruin Probability of a Discrete-Time Risk Process

Part of: Markov processes Special processes Mathematical economics

Published online by Cambridge University Press:  14 July 2016

Maikol A. Diasparra  and
Rosario Romera
Maikol A. Diasparra*
Affiliation:
Universidad Simón Bolívar
Rosario Romera*
Affiliation:
Universidad Carlos III de Madrid
*
∗Postal address: Department of Pure and Applied Mathematics, Universidad Simón Bolívar, 1080-A Caracas, Venezuela. Email address: [email protected]
∗∗Postal address: Department of Statistics, Universidad Carlos III de Madrid, 28903 Getafe, Spain. Email address: [email protected]
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Abstract

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We consider a discrete-time risk process driven by proportional reinsurance and an interest rate process. We assume that the interest rate process behaves as a Markov chain. To reduce the risk of ruin, we may reinsure a part or even all of the reserve. Recursive and integral equations for ruin probabilities are given. Generalized Lundberg inequalities for the ruin probabilities are derived given a stationary policy. To illustrate these results, a numerical example is included.

Keywords

Risk processruin probabilityLundberg's inequalityproportional reinsurance

MSC classification

Secondary: 91B30: Risk theory, insurance 60K10: Applications (reliability, demand theory, etc.) 60J05: Discrete-time Markov processes on general state spaces
Type
Research Article
Information
Journal of Applied Probability , Volume 46 , Issue 1 , March 2009 , pp. 99 - 112
Copyright
Copyright © Applied Probability Trust 2009 

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