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Ruin Problems: Simulation or Calculation?

Published online by Cambridge University Press:  10 June 2011

D.C.M. Dickson  and
H.R. Waters
D.C.M. Dickson
Affiliation:
Centre for Actuarial Studies, The University of Melbourne, Victoria, 3010, Australia. Tel: +61 3 8344 6899; E-mail: ddickson@cupid.ecom.unimelb.edu.au
H.R. Waters
Affiliation:
Heriot-Watt University, Riccarton, Edinburgh, EH14 4AS, U.K. Tel: +44 (0)131 451 3211; Fax: +44 (0)131 451 3249; E-mail: h.r.waters@ma.hw.ac.uk
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Abstract

In this paper we use a case study of a non-life insurance portfolio to demonstrate how recent research in ruin theory can be applied to solvency problems. By approximating the aggregate claims distribution for the portfolio by a translated gamma distribution, we estimate ruin probabilities through a recursive procedure when the insurer earns investment income on its surplus. We also show the results of applying simulation techniques to this problem, and discuss some advantages and disadvantages of simulation as a means of assessing ruin probabilities. Finally we discuss the calculation of the probability of ruin at the end of a specified time period.

Keywords

Ruin TheoryTranslated Gamma DistributionInvestment IncomeSimulationRecursive Calculation

Information

Type
Sessional meetings: papers and abstracts of discussions
Information
British Actuarial Journal , Volume 2 , Issue 3 , 01 August 1996 , pp. 727 - 740
Copyright
Copyright © Institute and Faculty of Actuaries 1996

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References

REFERENCES

Beard, R.E., Pentikäinen, T. & Pesonen, E. (1983). Risk theory (3rd edition). Chapman and Hall, London.Google Scholar
Daykin, C.D., Pentikäinen, T. & Pesonen, M. (1993). Practical risk theory for actuaries. Chapman and Hall, London.CrossRefGoogle Scholar
De Vylder, F. & Goovaerts, M.J. (1988). Recursive calculation of finite-time ruin probabilities. Insurance: Mathematics and Economics, 7, 1–7.Google Scholar
Dickson, D.C.M. & Waters, H.R. (1991). Recursive calculation of survival probabilities. ASTIN Bulletin, 21, 199–221.CrossRefGoogle Scholar
Dickson, D.C.M. & Waters, H.R. (1993). Gamma processes and finite time survival probabilities. ASTIN Bulletin, 23, 259–272.CrossRefGoogle Scholar
Dickson, D.C.M. & Waters, H.R. (1994). Reinsurance and ruin. To appear in Insurance: Mathematics and Economics.Google Scholar
Ramlau-Hansen, H. (1988a). A solvency study in non-life insurance. Part 1. Analysis of fire, windstorm and glass claims. Scandinavian Actuarial Journal, 3–34.CrossRefGoogle Scholar
Ramlau-Hansen, H. (1988b). A solvency study in non-life insurance. Part 2. Solvency margin requirements. Scandinavian Actuarial Journal, 35–59.CrossRefGoogle Scholar
Ramlau-Hansen, H. (1986). Statistical analysis of policy and claims data in non-life insurance; a solvency study. Part 1: Introduction to the study and analysis of glass claims. Working Paper No. 60 from the Laboratory of Actuarial Mathematics, University of Copenhagen.Google Scholar
Seal, H.L. (1969). Simulation of the ruin potential of non-life insurance companies. Transactions of the Society of Actuaries, 21, 563–590.Google Scholar
Sundt, B. (1993). An introduction to non-life insurance mathematics (3rd edition). Verlag Versicherungswirtschaft e.V. Karlsruhe.Google Scholar
Taylor, G.C. & Buchanan, R. (1988). The management of solvency. In Classical insurance solvency theory, Edited by Cummins, J.D. and Derrig, R.A.. Kluwer, London.Google Scholar
Wilkie, A.D. (1986). A stochastic investment model for actuarial use. T.F.A. 39, 341–373.Google Scholar