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HIV, AIDS and the approximate calculation of life insurance functions, annuities and net premiums

Published online by Cambridge University Press:  20 April 2012

S. Haberman
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Abstract

The paper presents an application of the Markov chain as a tool for the calculation of life contingencies functions (e.g. assurance, annuity, net premium, policy value functions) arising from a multi-state model which represents the transmission and development of HIV and AIDS. The transmission model advocated by the Institute of Actuaries AIDS Working Party is modified and simplified and then applied to derive explicit formulae for these standard life contingencies functions. This investigation allows a thorough review of the properties of these functions to be conducted and assists with the calculation of premiums and reserves in the presence of HIV and AIDS.

Keywords

HIVInsurance FunctionsMarkov Chain
Type
Research Article
Information
Journal of the Institute of Actuaries , Volume 119 , Issue 2 , 1992 , pp. 345 - 364
Copyright
Copyright © Institute and Faculty of Actuaries 1992

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References

REFERENCES

Daykin, C. D., Clark, P. N. S., Eves, M. J., Haberman, S., Le Grys, D. J., Lockyer, J., Michaelson, R. W. & Wilkie, A. D. (1988). The Impact of HIV Infection and AIDS on Insurance in the United Kingdom. J.I.A., 115, 727–837.Google Scholar
Daykin, C. D., Clark, P. N. S., Eves, M. J., Haberman, S., Le Grys, D. J., Lockyer, J., Michaelson, R. W. & Wilkie, A. D. (1990). Projecting the Spread of AIDS in the United Kingdom: A Sensitivity Analysis. J.I.A., 117, 95–133.Google Scholar
Forfar, D. O. & Waters, H. R. (1986). A Stochastic Approach to Life Contingencies. Institute of Actuaries Education Service Special Note, Oxford.Google Scholar
Frees, E. W. (1990). Stochastic Life Contingencies with Solvency Considerations. Trans. Soc. Ad., 42, 91–130 (with discussion).Google Scholar
Grimmett, G. R. & Stirzaker, D. R. (1982). Probability and Random Processes. Oxford University Press, Oxford.Google Scholar
Haberman, S. (1990). Actuarial Review of Models Describing and Predicting the Spread of HIV Infection and AIDS. J.I.A., 117, 319–405.Google Scholar
Hoem, J. M. (1988). Versatility of Markov Chain as a Tool in the Mathematics of Life Insurance. Introductory Lecture to Subject 3. Transactions of 23rd International Congress of Actuaries. Volume R. 171–202.Google Scholar
Neill, A. (1977). Life Contingencies. Heinemann, London.Google Scholar
Panjer, H. H. (1988). AIDS: Survival Analysis of Persons Testing HIV Positive. Trans. Soc. Act., 40, 517–530 (with discussion).Google Scholar
Ramsay, C. M. (1989). AIDS and the Calculation of Life Insurance Functions. Trans. Soc. Act., 41, 393–422 (with discussion).Google Scholar