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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 

References

[1] Asmussen, S (2000). Ruin Probabilities. World Scientific, River Edge, NJ.Google Scholar
[2] Cai, J. (2002). Ruin probabilities with dependent rates of interest. J. Appl. Prob. 39, 312–323.CrossRefGoogle Scholar
[3] Cai, J. and Dickson, D. C. M. (2004). Ruin probabilities with a Markov chain interest model. Insurance Math. Econom. 35, 513–525.CrossRefGoogle Scholar
[4] Grandell, J.} (1991). Aspects of Risk Theory. Springer, New York.Google Scholar
[5] González-Hernández, J., López-Martínez, R. R. and Pérez-Hernández, J. R. (2007). Markov control processes with randomized discounted cost. Math. Meth. Operat. Res. 65, 27–44.Google Scholar
[6] Hernández-Lerma, O. and Lasserre, J. B. (1996). Discrete-Time Markov Control Processes (Appl. Math. 30). Springer, New York.Google Scholar
[7] Hernández-Lerma, O. and Lasserre, J. B. (1999). Further Topics on Discrete-Time Markov Control Processes (Appl. Math. 42). Springer, New York.CrossRefGoogle Scholar
[8] Hernández-Lerma, O. and Lasserre, J. B. (2003). Markov Chains and Invariant Probabilities (Progress Math. 211). Birkhäuser, Basel.Google Scholar
[9] Schäl, M. (2004). On discrete-time dynamic programming in insurance: exponential utility and minimizing the ruin probability. Scand. Actuarial J. 3, 189–210.Google Scholar
[10] Schmidli, H. (2008). Stochastic Control in Insurance. Springer, London.Google Scholar
[11] Willmot, G. E. and Lin, X. S. (2001). Lundberg Approximations for Compound Distributions with Insurance Applications (Lectures Notes Statist. 156). Springer, New York.CrossRefGoogle Scholar