Orderings of risks: A comparative study via stop-loss transforms

Insurance: Mathematics and Economics

Volumn 17, Issue 3, 1996, Pages 215-222

  Müller, Alfred ^a  

^a UNIVERSITY OF KARLSRUHE   (Germany)

Author keywords

Convex order; More dangerous; Order lattices; Stochastic dominance; Stop loss convergence; Stop loss order; Stop loss transform

Indexed keywords

EID: 0030119941     PISSN: 01676687     EISSN: None     Source Type: Journal    
DOI: 10.1016/0167-6687(96)90002-5     Document Type: Article

References (21)

1. Bühlmann, H., B. Gagliardi, H.U. Gerber and E. Straub (1977). Some inequalities for stop-loss premiums. ASTIN Bulletin 9, 75-83.
2. De Groot, M.H. (1970). Optimal Statistical Decisions. MacGraw-Hill, New York.
3. Elton, J. and T.P. Hill (1992). Fusions of a probability distribution. Annals of Probability 20, 421-454.
4. Goovaerts, M.J., R. Kaas, A.E. van Heerwaarden and T. Bauwelinckx (1990). Effective Actuarial Methods. North-Holland, Amsterdam.
5. Heilmann, W.R. and K.J. Schröter (1991). Orderings of risks and their actuarial applications. In: K. Mosler and M. Scarsini, (eds.), Stochastic Orders and Decision under Risk. IMS Lecture Notes-Monograph Series, Vol. 19, pp. 157-173.
6. Kaas, R. and A.E. van Heerwaarden (1992). Stop-loss order, unequal means, and more dangerous distributions. Insurance: Mathematics and Economics 11, 71-77.
7. Karlins, S. and A. Novikoff (1963). Generalized convex inequalities. Pacific Journal of Mathematics 13, 1251-1279.
8. Kertz, R.P. and U. Rösler (1992). Stochastic and convex orders and lattices of probability measures. Israel Journal of Mathematics 77, 129-164.
9. Lehmann, E. (1955). Ordered families of distributions. Annals of Mathematical Statistics 26, 399-419.
10. Makowski, A.M. (1994). On an elementary characterization of the increasing convex ordering, with an application. Journal of Applied Probability 31, 834-840.
11. Ohlin, J. (1969). On a class of measures for dispersion with application to optimal insurance. ASTIN Bulletin 5, 249-266.
12. Rockafellar, R.T. (1970). Convex Analysis. Princeton Univ. Press, Princeton, New Jersey.
13. Rolski, T. (1976). Order relations in the set of probability distribution functions and their applications in queueing theory. Dissertationes Mathematicae 132.
14. Ross, S.M. (1983). Stochastic Processes. Wiley, New York.
15. Rothschild, M. and J.E. Stiglitz (1970). Increasing risk, I: A definition. Journal of Economic Theory 2, 225-243.
16. Shaked, M. and J.G. Shanthikumar (1994). Stochastic orders and their Applications. Academic Press, London.
17. Stoyan, D. (1973). Bounds for the extrema of the expected value of a convex function of independent random variables. Studia Scientiarum Mathematicarum Hungarica 8, 153-159.
18. Stoyan, D. (1983). Comparison Methods for Queues and Other Stochastic Models. Wiley, Chichester.
19. Strassen, V. (1965). The existence of probability measures with given marginals. Annals of Mathematical Statistics 36, 423-439.
20. Sundt, B. (1991). An Introduction to Non-Life Insurance Mathematics. Verlag Versicherungswirtschaft e.V., Karlsruhe.
21. van Heerwaarden, A.E. (1991). Ordering of risks: Theory and Actuarial Applications. Tinbergen Institute Series no. 20. Thesis Publishers, Amsterdam.