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Threshold strategies for risk processes and their relation to queueing theory

Part of: Mathematical economics Special processes

Published online by Cambridge University Press:  14 July 2016

Onno J. Boxma ,
Andreas Löpker  and
David Perry
Onno J. Boxma
Affiliation:
Eindhoven University of Technology, Department of Mathematics and Computer Science, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands. Email address: boxma@win.tue.nl
Andreas Löpker
Affiliation:
Eindhoven University of Technology, Department of Economics and Social Sciences, Helmut Schmidt University, Postfach 700822, 22008 Hamburg, Germany
David Perry
Affiliation:
University of Haifa, Department of Statistics, University of Haifa, Haifa 31905, Israel
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Abstract

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We consider a risk model with threshold strategy, where the insurance company pays off a certain percentage of the income as dividend whenever the current surplus is larger than a given threshold. We investigate the ruin time, ruin probability, and the total dividend, using methods and results from queueing theory.

Keywords

QueueM/G/1G/M/1risk processruin theorythreshold strategydividend

MSC classification

Primary: 60K25: Queueing theory 91B30: Risk theory, insurance
Secondary: 60K30: Applications (congestion, allocation, storage, traffic, etc.)

Information

Type
Part 1. Risk Theory
Information
Journal of Applied Probability , Volume 48 , Issue A: New Frontiers in Applied Probability (Journal of Applied Probability Special Volume 48A) , August 2011 , pp. 29 - 38
Copyright
Copyright © Applied Probability Trust 2011 

References

[1] Adan, I., Boxma, O. and Perry, D., (2005). The G/M/1 queue revisited. Math. Meth. Operat. Res. 62, 437–452.CrossRefGoogle Scholar
[2] Asmussen, S. and Petersen, S. S., (1988). Ruin probabilities expressed in terms of storage processes. Adv. Appl. Prob. 20, 913–916.CrossRefGoogle Scholar
[3] Cohen, J. W., (1982). The Single Server Queue (N. Holland Ser. Appl. Math. Mech. 8). North-Holland, Amsterdam.Google Scholar
[4] Gaver, D. P. Jr. and Miller, R. G. Jr., (1962). Limiting distributions for some storage problems. In Studies in Applied Probability and Management Science, Stanford University Press, pp. 110–126.Google Scholar
[5] Gerber, H. U. and Shiu, E. S. W., (2006). On optimal dividend strategies in the compound Poisson model. N. Amer. Actuarial J. 10, 76–93.CrossRefGoogle Scholar
[6] Li, S. and Garrido, J., (2004). On a class of renewal risk models with a constant dividend barrier. Insurance Math. Econom. 35, 691–701.CrossRefGoogle Scholar
[7] Lin, X. S. and Pavlova, K. P., (2006). The compound Poisson risk model with a threshold dividend strategy. Insurance Math. Econom. 38, 57–80.CrossRefGoogle Scholar
[8] Lin, X. S., Willmot, G. E. and Drekic, S., (2003). The classical risk model with a constant dividend barrier: analysis of the Gerber–Shiu discounted penalty function. Insurance Math. Econom. 33, 551–566.Google Scholar
[9] Löpker, A. and Perry, D., (2010). The idle period of the finite G/M/1 queue with an interpretation in risk theory. Queueing Systems 64, 395–407.CrossRefGoogle Scholar
[10] Perry, D., Stadje, W. and Zacks, S., (2000). Busy period analysis for M/G/1 and G/M/1 type queues with restricted accessibility. Operat. Res. Lett. 27, 163–174.CrossRefGoogle Scholar
[11] Prabhu, N. U., (1997). Stochastic Storage Processes, 2nd edn. Springer, New York.Google Scholar