Upper and lower bounds for sums of random variables

Insurance: Mathematics and Economics

Volumn 27, Issue 2, 2000, Pages 151-168

  Kaas, Rob ^a,b   Dhaene, Jan ^a,b   Goovaerts, Marc J ^a,b  

^a UNIVERSITY OF AMSTERDAM   (Netherlands)

^b UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

Cash flows; Comonotonicity; Convex order; Dependent risks; Present values; Stochastic annuities

Indexed keywords

EID: 0000986511     PISSN: 01676687     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-6687(00)00060-3     Document Type: Article

References (19)

1. Bäuerle N., Müller A. Modeling and comparing dependencies in multivariate risk portfolios. ASTIN Bulletin. 28:1998;59-76.
2. Brockett P., Garven J. A reexamination of the relationship between preferences and moment orderings by rational risk averse investors. Geneva Papers on Risk and Insurance Theory. 23:1998;127-137.
3. Denuit M., Lefèvre C. Stochastic product orderings, with applications in actuarial sciences. Bulletin Français d'Actuariat. 1:1997;61-82.
4. Denuit M., De Vylder F., Lefèvre C. Extrema with respect to. s -convex orderings in moment spaces: a general solution Insurance: Mathematics and Economics. 24:1999;201-217.
5. Dhaene J., Denuit M. The safest dependency structure among risks. Insurance: Mathematics and Economics. 25:1999;11-21.
6. Dhaene J., Goovaerts M. Dependency of risks and stop-loss order. ASTIN Bulletin. 26:1996;201-212.
7. Dhaene J., Goovaerts M.J. On the dependency of risks in the individual life model. Insurance: Mathematics and Economics. 19:1997;243-253.
8. Dhaene, J., Wang, S., Young, V., Goovaerts, M.J., 1998. Comonotonicity and maximal stop-loss premiums. Research Report 9730. DTEW, KU Leuven, p. 13, submitted for publication.
9. Goovaerts M.J., Redant R. On the distribution of IBNR reserves. Insurance: Mathematics and Economics. 25:1999;1-9.
10. Goovaerts M.J., Dhaene J., De Schepper A. Stochastic upper bounds for present value functions. Journal of Risk and Insurance Theory. 67.1:2000;1-14.
11. Kaas R. How to (and how not to) compute stop-loss premiums in practice. Insurance: Mathematics and Economics. 13:1994;241-254.
12. Kaas, R., Van Heerwaarden, A.E., Goovaerts, M.J., 1994. Ordering of actuarial risks. Institute for Actuarial Science and Econometrics, University of Amsterdam, Amsterdam, p. 144.
13. Müller A. Stop-loss order for portfolios of dependent risks. Insurance: Mathematics and Economics. 21:1997;219-223.
14. Rogers L.C.G., Shi Z. The value of an Asian option. Journal of Applied Probability. 32:1995;1077-1088.
15. Shaked, M., Shanthikumar, J.G., 1994. Stochastic Orders and Their Applications. Academic Press, New York, p. 545.
16. Simon S., Goovaerts M.J., Dhaene J. An easy computable upper bound for the price of an arithmetic Asian option. Insurance: Mathematics and Economics. 26.2-3:2000;175-184.
17. Vyncke, D., Goovaerts, M.J., Dhaene, J., 2000. Convex upper and lower bounds for present value functions, Research Report 0025, Dept. of Applied Economics, KU Leuven, Belgium.
18. Wang S., Dhaene J. Comonotonicity, correlation order and stop-loss premiums. Insurance: Mathematics and Economics. 22(3):1998;235-243.
19. Wang S., Young V. Ordering risks: expected utility versus Yaari's dual theory of choice under risk. Insurance: Mathematics and Economics. 22:1998;145-162.