The present value of a stochastic perpetuity and the Gamma distribution

Insurance: Mathematics and Economics

Volumn 20, Issue 3, 1997, Pages 243-250

  Milevsky, Moshe Arye ^a  

^a YORK UNIVERSITY   (Canada)

Author keywords

Endowments; Martingales; Stochastic calculus

Indexed keywords

EID: 0031572647     PISSN: 01676687     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-6687(97)00013-9     Document Type: Article

References (18)

1. Beekman, J.A. and C.P. Fuelling (1993). One approach to dual randomness in life insurance. Scandinavian Actuarial Journal 12, 173-182.
2. Beekman, J.A. and C.P. Fuelling (1990). Interest and mortality randomness in some annuities. Insurance: Mathematics and Economics 9, 185-196.
3. Beekman, J.A. and C.P. Fuelling (1991). Extra randomness in certain annuity models. Insurance: Mathematics and Economics 10, 275-287.
4. Boyle, P.P. (1976). Rates of return as random variables. Journal of Risk and Insurance 43, 693-713.
5. Buhlmann, H. (1992). Stochastic discounting. Insurance: Mathematics and Economics 11, 113-127.
6. DeSchepper, A., F. DeVylder, M. Goovaerts and R. Kaas (1992). Interest randomness in annuities certain. Insurance: Mathematics and Economics 11 (3), 271-282.
7. DeSchepper, A., M. Teunen and M. Goovaerts (1994). An analytic inversion of a laplace transform related annuities certain. Insurance: Mathematics and Economics 14, 33-37.
8. Dhaene, J. (1989). Stochastic interest rates and autoregressive integrated moving average processes. ASTIN Bulletin 19 (2), 131-138.
9. Dufresne, D. (1989). Stability of Pension systems when rates of return are random. Insurance: Mathematics and Economics 8, 71-76.
10. Dufresne, D. (1990). The distribution of a Perpetuity with applications to risk theory and pension funding. Scandinavian Actuarial Journal 9, 39-79.
11. Giaccotto, C. (1986). Stochastic modeling of interest rates: Actuarial vs. equilibrium approach. Journal of Risk and Insurance 53 (3), 435-453.
12. Karatzas, I. and S.E. Shreve (1992). Bronwian Motion and Stochastic Calculus, 2nd Ed. (Springer, Berlin).
13. Panjer, H. and D. Bellhouse (1980). Stochastic modeling of interest rates with applications to life contingencies. Journal of Risk and Insurance 47, 91-110.
14. Parker, G. (1993). Distribution of the present value of future cash flows. Proceedings of the 3rd Annual AFIR Collopium, 832-843.
15. Parker, G. (1994). Stochastic analysis of a portfolio of endowment insurance policies. Scandinavian Actuarial Journal 2, 119-130.
16. Parker, G. (1995). A second order stochastic differential equation for the force of interest. Insurance: Mathematics and Economics 16, 211-224.
17. Vanneste, M., M. Goovaerts, A. DeSchepper and J. Dhaene (1997). A straightforward analytic calculation of the distribution of an annuity certain with stochastic interest rate. Insurance: Mathematics and Economics, to appear.
18. Vanneste, M., M. Goovaerts and E. Labie (1994). The distribution of annuities. Insurance: Mathematics and Economics 15 (1) 37-48.