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Should Actuaries be Random?

Published online by Cambridge University Press:  11 August 2014

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The aims of this paper are twofold:

(a) To act as a guide to the basic mathematics and methods of simulation which might be useful to actuaries.

(b) To describe how simulation techniques might be used by actuaries, to promote a discussion about whether the suggested approaches are worth pursuing and to encourage people to suggest other possible actuarial uses for simulation.

Section 2 of the paper outlines the general methodology of simulation and serves as a guide to those appendices of the paper where some technical details are given.

Section 3 of the paper considers various actuarial problems and discusses how simulation methods might be applied to them. We have not worked on all the problems described in this section ourselves. The intention is partly to suggest problems that could be tackled by simulation and to consider whether this approach is worthwhile.

Type
Research Article
Copyright
Copyright © Institute of Actuaries Students' Society 1982

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References

REFERENCE

(1.1) Atkinson, A. C. (1980) ‘Test of Pseudo-random NumbersJ.R.S.S. (C), 29, 164.Google Scholar
(1.2) Knuth, D. E. (1969) The Art of Computer Programming, Vol. 2, Seminumerical Algorithms. Addison-Wesley, Reading, MasGoogle Scholar
(2.1) Atkinson, A. C. (1980) ‘Tests of pseudo-random numbersJ.R.S.S. (C), 29, 2.Google Scholar
(2.2) Chay, S. C, Fardo, R. D. and Mazumdar, M. (1975) ‘On using the Box-Miiller transformation with congruential pseudo-random number generatorsJ.R.S. (C), 24, 1.Google Scholar
(2.3) Golder, E. R. (1976) ‘Spectral test for evaluation of congruential pseudo-random generators AS98J.R.S.S. (C), 25, 2.Google Scholar
(2.4) Knuth, D. E. (1969) The Art of Computer Programming, Vol. 2, Seminumerical Algorithms Addison-Wesleyy, Reading, Mass.Google Scholar
(2.5) Neave, H. R. (1973) ‘On using the Box-Miiller transformation with multiplicative congruential pseudo-random number generatorsJ.R.S.S. (C), 22, 1.Google Scholar
(2.6) Wedderburn, R. W. M. (1976) A remark on AS29 ‘The Runs Up and Down TestJ.R.S.S. (C), 25, 2.Google Scholar
(3.1) Atkinson, A. C. and Pearce, M. C. (1976) ‘Computer Generation of Beta, Gamma and Normal Random VariablesJ.R.S.S. (A), 139, Part 4.Google Scholar
(3.2) Knuth, D. E. (1969) The Art of Computer Programming, Vol. 2, Seminumerical Algorithms. Addison-Wesley, Reading, Mass.Google Scholar
(3.3) Benjamin, S.Putting Computers on to Actuarial Work', Appendix 2. J.I.A. 92, 134.Google Scholar
(3.4) ‘Report of the Maturity Guarantees Working PartyJ.I.A. 107, 103.Google Scholar
(3.5) Kendall, M. G. and Stuart, A. (1969) The Advanced Theory of Statistics. Vol. 1, Griffin, London.Google Scholar
(3.6) Atkinson, A. C.The Computer Generation of Poisson Random VariablesJ.R.S.S. (C), 28, 1.Google Scholar
(3.7) Atkinson, A. C.Recent Developments in the Computer Generation of Poisson Random VariablesJ.R.S.S. (C), 28, 3.Google Scholar
(3.8) Aitchison, J. and Brown, J. A. C. (1963) The Lognormal Distribution. University Press, Cambridge.Google Scholar
(3.9) Johnson, N. L. and Kotz, S. (1970) Continuous Univariate Distributions—1. Houghton Mifflin, Boston.Google Scholar
(3.10) Apostol, T. (1957) Mathematical Analysis. Addison-Wesley.Google Scholar
(4.1) Kendall, M. G. and Stuart, A. (1972) The Advanced Theory of Statistics Vol. 2. Griffin, London.Google Scholar
(4.2) Biometrika Tables for Statisticians (1976) Vol 2. Griffin, London.Google Scholar
(5.1) Kleijnen, J. P. C. (1975) Statistical Techniques in Simulation, Parts I and II. Dekker, New York.Google Scholar
(5.2) Kendall, M. G. and Stuart, A. (1973) The Advanced Theory of Statistics, Vol. 2, Vol. 3. Griffin, London.Google Scholar
(5.3) Report of the Maturity Guarantees Working Party J.I.A. 107, 103.Google Scholar
(5.4) Simon, G. (1976) ‘Computer simulation swindles with applications to estimates of location and dispersionJ.R.S.S. (C), 25, 3.Google Scholar
(6.1) Kendall, M. G. and Stuart, A. (1972) The Advanced Theory of Statistics, Vol. 2. Griffin, London.Google Scholar
(6.2) Kleijnen, J. P. C. (1975) Statistical Techniques in Simulation. Dekker, New York.Google Scholar
(7.1) Benjamin, S. (1966) ‘Putting Computers on to Actuarial WorkJ.I.A. 92, 134.Google Scholar
(7.2) Benjamin, S. (1964) Simulating Mortality Fluctuations. Transactions of the 17th International Congress of Actuaries, 3, II, 478.Google Scholar
(7.3) Seal, H. L. (1978) Survival Probabilities. Wiley, Chichester.Google Scholar
Beard, R. E., Pentikainen, T. and Pesonen, E. (1977) Risk Theory. 2nd Ed, Chapman and Hall, London.CrossRefGoogle Scholar