On life insurance reserves in a stochastic mortality and interest rates environment

Insurance: Mathematics and Economics

Volumn 25, Issue 3, 1999, Pages 261-280

  Marceau, Etienne ^a   Gaillardetz, Patrice ^a  

^a UNIVERSITÉ LAVAL   (Canada)

Author keywords

IB11; IM01; IM40; Prospective reserves; Stochastic interest; Stochastic mortality

Indexed keywords

EID: 0011994751     PISSN: 01676687     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-6687(99)00019-0     Document Type: Article

References (29)

1. Beekman J.A., Fuelling C.P. Interest and mortality randomness in some annuities. Insurance: Mathematics and Economics. 10:1991;275-287.
2. Bellhouse D.R., Panjer H.H. Stochastic modelling of interest rates with applications to life contingencies - Part II. Journal of Risk and Insurance. 47:1981;628-637.
3. Boyle P.P. Rates of return as random variables. Journal of Risk and Insurance. 43:1976;693-713.
4. Bowers, N.L., Gerber, H.U., Hickman, J.C., Jones, D.A., Nesbitt, C.J., 1997. Actuarial Mathematics. Schaumburg, Ill: Society of Actuaries.
5. De Schepper A., Goovaerts M. Some further results on annuities certain with random interest. Insurance: Mathematics and Economics. 11:1992;283-290.
6. De Schepper A., Teunen M., Goovaerts M. Some further results on annuities certain with random interest. Insurance: Mathematics and Economics. 14:1994;33-37.
7. Devolder, P., 1986. Operations stochastiques de capitalisation. ASTIN Bulletin 16S, S5-S30.
8. DeVylder, F., 1997. Life Insurance Theory (Actuarial Perspectives). Kluwer Academic Publishers, Boston.
9. Dhaene J. Stochastic interest rates and autoregressive integrated moving average processes. ASTIN Bulletin. 19:1989;131-138.
10. Dhaene J. Actuarial functions and random rates of return. Bulletin of the Royal Society of Belgian Actuaries. 85:1992;23-36.
11. Dufresne, D., 1990. The distribution of a perpetuity, with applications to risk theory and pension funding. Scandinavian Actuarial Journal, 39-79.
12. Frees E.W. Stochastic life contingencies with solvency considerations (with discussions). Transactions of the Society of Actuaries. 42:1990;911-948.
13. Gerber, H.U., 1997. Life Insurance Mathematics. Springer, New York.
14. Lai S.L., Frees E. Examining changes in reserves using stochastic interest models. Journal of Risk and Insurance. 62:1995;535-574.
15. Milevsky, M.A., Posner, S.E., 1998. Asian options, the sum of lognormals, and the reciprocal gamma distribution. Journal of Financial and Quantitative Analysis, forthcoming.
16. Norberg, R., 1991. Reserves in life and pension insurance, Scandinavian Actuarial Journal, 3-24.
17. Norberg, R., 1993. A solvency study in life insurance, Proceedings of the third AFIR International Colloquium, Rome, 822-830.
18. Norberg R. A continuous-time Markov chain interest model with applications to insurance. Journal of Applied Stochastic Models and Data Analysis. 11:1995;245-256.
19. Norberg, R., 1997a. Bonus in Life Insurance: Principles and Prognoses in a Stochastic Environment, Working Paper no. 142, Laboratory of Actuarial Mathematics.
20. Norberg, R., 1997b. Discussion in: Parker, G. (1997), Stochastic Analysis of the Interaction between Investment and Insurance Risks.
21. Panjer H.H., Bellhouse .R. Stochastic modelling of interest rates with applications to life contingencies. Journal of Risk and Insurance. 47:1980;91-110.
22. Parker, G., 1994a. Moments of the present value of a portfolio of policies. Scandinavian Actuarial Journal, 53-67.
23. Parker G. Limiting distribution of the present value of a portfolio. ASTIN Bulletin. 24:1994b;47-60.
24. Parker, G., 1994c. Stochastic analysis of a portfolio of endowment policies. Scandinavian Actuarial Journal, 119-130.
25. Parker G. A portfolio of endownment policies and its limiting distribution. ASTIN Bulletin. 26:1996;25-34.
26. Parker G. Stochastic analysis of the interaction between investment and insurance risks. North American Actuarial Journal. 1:1997;55-84.
27. Shiriayev, A.N., 1996. Probability. Springer, New York.
28. Vanneste M., Goovaerts M., DeSchepper A., Dhaene J. A straightforward analytic calculation of the distribution of annuity certain with stochastic interest rates. Insurance: Mathematics and Economics. 20:1997;35-41.
29. Waters H.R. The moments and distributions of actuarial functions. Journal of the Institute of Actuaries. 105:1978;61-75.