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Randomized Observation Periods for the Compound Poisson Risk Model: Dividends

Published online by Cambridge University Press:  09 August 2013

Hansjörg Albrecher ,
Eric C.K. Cheung  and
Stefan Thonhauser
Hansjörg Albrecher
Affiliation:
Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne, Faculty Member of the Swiss Finance Institute UNIL-Dorigny, CH-1015 Lausanne, Switzerland
Eric C.K. Cheung
Affiliation:
Department of Statistics and Actuarial Science, University of Hong Kong, Pokfulam, Hong Kong
Stefan Thonhauser
Affiliation:
Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne, UNIL-Dorigny, CH-1015 Lausanne, Switzerland
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Abstract

In the framework of the classical compound Poisson process in collective risk theory, we study a modification of the horizontal dividend barrier strategy by introducing random observation times at which dividends can be paid and ruin can be observed. This model contains both the continuous-time and the discrete-time risk model as a limit and represents a certain type of bridge between them which still enables the explicit calculation of moments of total discounted dividend payments until ruin. Numerical illustrations for several sets of parameters are given and the effect of random observation times on the performance of the dividend strategy is studied.

Keywords

Compound Poisson risk modelhorizontal dividend barrier strategyErlangization
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 41 , Issue 2 , November 2011 , pp. 645 - 672
Copyright
Copyright © International Actuarial Association 2011

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References

[1] Albrecher, H., Cheung, E.C.K. and Thonhauser, S. (2011) Randomized observation periods for the compound Poisson risk model: The Discounted Penalty Function. Scandinavian Actuarial Journal, to appear.Google Scholar
[2] Albrecher, H., Claramunt, M.M. and Marmol, M. (2005) On the distribution of dividend payments in a Sparre Andersen model with generalized Erlang(n) interclaim times. Insurance: Mathematics and Economics 37(2): 324–334.Google Scholar
[3] Albrecher, H. and Hartinger, J. (2007) A risk model with multi- layer dividend strategy. North American Actuarial Journal 11(2): 43–64.Google Scholar
[4] Asmussen, S. and Albrecher, H. (2010) Ruin Probabilities. Second Edition, World Scientific, New Jersey.CrossRefGoogle Scholar
[5] Asmussen, S. Avram, F. and Usabel, M. (2002) Erlangian approximations for finite-horizon ruin probabilities. ASTIN Bulletin 32(2): 267–281.Google Scholar
[6] Avanzi, B., Gerber, H.U. and Shiu, E.S.W. (2007) Optimal dividends in the dual model. Insurance: Mathematics and Economics 41(1): 111–123.Google Scholar
[7] Dickson, D.C.M. and Waters, H.R. (2004) Some optimal dividends problems. ASTIN Bulletin 34(1): 49–74.Google Scholar
[8] Gerber, H.U., Lin, X.S. and Yang, H. (2006) A note on the dividends-penalty identity and the optimal dividend barrier. ASTIN Bulletin 36(2): 489–503.Google Scholar
[9] Gerber, H.U. and Shiu, E.S.W. (1998) On the time value of ruin. North American Actuarial Journal 2(1): 48–72.Google Scholar
[10] Gerber, H.U. and Shiu, E.S.W. (2005) The time value of ruin in a Sparre Andersen model. North American Actuarial Journal 9(2): 49–69.CrossRefGoogle Scholar
[11] Gerber, H.U. and Shiu, E.S.W. (2006) On optimal dividend strategies in the compound Poisson model. North American Actuarial Journal 10(2): 76–93.Google Scholar
[12] Lin, X.S. and Sendova, K.P. (2008) The compound Poisson risk model with multiple thresholds. Insurance: Mathematics and Economics 42(2): 617–627.Google Scholar
[13] Ramaswami, V., Woolford, D.G. and Stanford, D.A. (2008) The Erlangization method for Markovian fluid flows. Annals of Operations Research 160(1): 215–225.Google Scholar
[14] Rolski, T., Schmidli, H., Schmidt, V. and Teugels, J. (1999) Stochastic processes for Insurance and Finance, John Wiley & Sons Ltd., Chichester.CrossRefGoogle Scholar
[15] Shimizu, Y. (2009) A new aspect of a risk process and its statistical inference. Insurance: Mathematics and Economics 44(1): 70–77.Google Scholar
[16] Stanford, D.A., Avram, F., Badescu, A.L., Breuer, L., Da Silva Soares, A. and Latouche, G. (2005) Phase-type approximations to finite-time ruin probabilities in the Sparre-Anderson and stationary renewal risk models. ASTIN Bulletin 35(1): 131–144.Google Scholar
[17] Stanford, D.A., Yu, K. and Ren, J. (2011) Erlangian approximation to finite time ruin probabilities in perturbed risk models. Scandinavian Actuarial Journal 2011(1): 38–58.Google Scholar