Lorenz and excess wealth orders, with applications in reinsurance theory

Scandinavian Actuarial Journal

Volumn 1999, Issue 2, 1999, Pages 170-185

  Denuit, Michel ^a   Vermandele, Catherine ^a  

^a UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

Author keywords

Arrow Ohlin theorem; Convex order; Dispersive order; Excess wealth; Lorenz order; Optimal reinsurance; Order loss ratios; Stochastic dominance; Stop loss order; Vajda Ohlin theorem

Indexed keywords

EID: 84963530106     PISSN: 03461238     EISSN: 16512030     Source Type: Journal    
DOI: 10.1080/03461239950132642     Document Type: Article

References (41)

1. Arnold, B. C. (1987). Majorization and the Lorenz order: a brief introduction. Lecture notes in statistics 43. Springer Verlag, Berlin.
2. Arnold, B. C. (1991). Preservation and attenuation of inequality as measured by the Lorenz order. In: Stochastic orders and decisions under risk. Eds: K. Mosler and M. Scarsini. Hayward, California, IMS Lecture Notes-Monograph Series, 19, 25-37.
3. Belzunce, F. (1998). On a characterization of right spread order by the increasing convex order. Technical Report, Dpto Estadica e I.O., Universidad de Murcia.
4. Borch, K. (1961). The utility concept applied to the theory of insurance. ASTIN Bulletin 1, 245-255.
5. Bühlmann, H., Gagliardi, B., Gerber, H. & Straub, E. (1977). Some inequalities for stop-loss premiums. ASTIN Bulletin 9, 75-83.
6. Denuit, M. & Lefèvre, C. (1997). Some new classes of stochastic order relations among arithmetic random variables with applications in actuarial sciences. Insurance: Mathematics and Economics 20, 197-214.
7. Denuit, M., Lefèvre, C. & Shaked, M. (1997). The s-convex orders among real random variables, with applications. Mathematical Inequalities and Their Applications. In press.
8. Denuit, M. & Vermandele, C. (1998). Optimal reinsurance and stop-loss order. Insurance: Mathematics and Economics 22, 229-233.
9. Doherty, T. V. (1980). Stochastic ordering of risk:insurance exchanges. Scandinavian Actuarial Journal, 203-208.
10. Doherty, N. A. & Eeckhoudt, L. (1995). Optimal insurance without expected utility: the dual theory and the linearity of insurance contracts. Journal of Risk and Uncertainty 10, 157-179.
11. Eeckhoudt, L., Gollier, C. & Schlesinger, H. (1991). Increases in risk and deductible insurance. Journal of Economic Theory 55, 435-440.
12. Fagiuoli, E., Pellerey, F. & Shaked, M. (1997). A characterization of the dilation order and its applications. Technical Report. Department of Mathematics, The University of Arizona.
13. Fernandez-Ponce, J. M., Kochar, S. C. & Munoz-Perez, J. (1997). Partial ordering of distributions based on right spread functions. Journal of Applied Probability. In press.
14. Gollier, Ch. (1992). Economic theory of risk exchanges: a review. In: Contributions to insurance economics. Ed: G. Dionne, Kluwer Academic Publishers, Boston, pp. 3-23.
15. Goovaerts, M. J., De Vylder, F. & Haezendonck, J. (1982). Ordering of risks: a review. Insurance: Mathematics and Economics 1, 131-163.
16. Goovaerts, M. J., Kaas, R., Van Heerwaarden, A. E. & Bauwelinckx, T. (1990). Effective actuarial methods. North-Holland, Amsterdam.
17. Hardy, G. H., Littlewood, J. E. & Pólya, G. (1929). Some simple inequalities satisfied by convex functions. Messenger Mathematics 58, 145-152.
18. Heilmann, W.-R. (1985). Transformations of claim distributions. Mitteilungen der Vereinigung schweiz. Versicherungsmathematiker, 57-69.
19. Heilmann, W.-R. (1986). Ordering of distributions and risk measurement. Blätter der Deutschen Gesellschaft für Versicherungsmathematik 17, 225-235.
20. Heilmann, W.-R. & Schröter, K.J. (1991). Orderings of risks and their actuarial applications. In: Stochastic orders and decisions under risk. Eds: K. Mosler and M. Scarsini, Hayward, California, IMS Lecture Notes-Monograph Series, 19, 157-173.
21. Hesselager, O. (1993). Extensions of Ohlin's lemma with applications to optimal reinsurance structures. Insurance: Mathematics and Economics 13, 83-97.
22. Hürlimann, W. (1992). Ordering of risks through loss ratios. Insurance: Mathematics and Economics 11, 49-54.
23. Hürlimann, W. (1995). Transforming, ordering and rating risks. Mitteilungen der Vereinigung schweiz. Versicherungsmathematiker, 213-236.
24. Hürlimann, W. (1996). Improved analytical bounds for some risk quantities. ASTIN Bulletin 26, 185-199.
25. Jewitt, I. (1989). Choosing between risky prospects: the characterization of comparative static results and location independent risks. Management Science 35, 60-70.
26. Kaas, R. & Hesselager, O. (1995). Ordering claim size distributions and mixed Poisson probabilities. Insurance: Mathematics and Economics 17, 193-201.
27. Kaas, R., Van Heerwaarden, A. E. & Goovaerts, M. J. (1994). Ordering of actuarial risks. CAIRE, Brussels.
28. Karamata, J. (1932). Sur une inégalité relative aux fonctions convexes. Publications Mathématiques de l'Université de Belgrade 1, 145-148.
29. Landsberger, M. & Meilijson, I. (1994). The generating process and an extension of Jewitt's location independent risk concept. Management Science 40, 662-669.
30. Lemaire, J. (1991). Borch's thoerem: a historical survey of applications. In: Risk, Information and Insurance. Ed: H. Louberge, Kluwer Academic Publishers, Boston, pp. 15-36.
31. Mack, T. (1985). The utility of deductibles from the insurer's point of view. Insurance: Mathematics and Economics 4, 75-79.
32. Meilijson, I. & Nádas, A. (1979). Convex majorization with an application to the length of critical paths. Journal of Applied Probability 16, 671-677.
33. Müller, A. (1996). Ordering of risks: A comparative study via stop-loss transforms. Insurance: Mathematics and Economics 17, 215-222.
34. Munoz-Perez, J. M. (1990). Dispersive ordering by the spread function. Statistics and Probability Letter 10, 407-410.
35. O'Cinneide, C. A. (1991). Phase-type distributions and majorization. The Annals of Applied Probability 1, 219-227.
36. Pham, T. G. & Turkkan, N. (1994). The Lorenz and the scaled total-time-on-test transform curves: a unified approach. IEEE Transactions on Reliability 43, 76-84.
37. Shaked, M. & Shanthikumar, J.G. (1994). Stochastic orders and their applications. Academic Press, New York.
38. Shaked, M. & Shanthikumar, J. G. (1998). Two variability orders. Probability in the Engineering and Informational Sciences 12, 1-23.
39. Spaeter, S. & Roger, P. (1997). The design of optimal insurance contracts: a topological approach. The Geneva Papers on Risk and Insurance Theory 22, 5-20.
40. Van Heerwaarden, A. E., Kaas, R. & Goovaerts, M.J. (1989). Optimal reinsurance in relation to ordering of risks. Insurance: Mathematics and Economics 8, 11-17.
41. Wilfling, B. (1996). Lorenz ordering of power-functions order statistics. Statistics and Probabilty Letters 30, 313-319.