Equilibrium Pricing Transforms: New Results Using Buhlmann's 1980 Economic Model

ASTIN Bulletin

Volumn 33, Issue 1, 2003, Pages 57-73

  Wang, Shaun S ^a  

^a SCOR Reinsurance Company   (United States)

Author keywords

Distorted Probability; Equilibrium Pricing; Esscher Transform; Exponential Tilting; Optimal Exchange; Wang Transform

Indexed keywords

EID: 85011436963     PISSN: 05150361     EISSN: 17831350     Source Type: Journal    
DOI: 10.1017/S0515036100013301     Document Type: Article

References (29)

1. Aase, K.K. (1993) Equilibrium in reinsurance syndicate; existence, uniqueness and characterization, ASTIN Bulletin. 23, 185–211.
2. Artzner, P., Delbaen, F., Eber, J-M. and Heath, D. (1999) Coherent measures of risk, Math. Finance. 9/3, 203–228.
3. Borch, K. (1962) Equilibrium in a reinsurance market, Econometrica. 30, 424–444.
4. Buhlmann, H. (1980) An economic premium principle, ASTIN Bulletin. 11, 52–60.
5. Buhlmann, H. (1984) The general economic premium principle. ASTIN Bulletin. 14, 13–21.
6. Buhlmann, H., Delbaen, F., Embrechts, P. and Shiryaev, A. (1998) On Esscher transforms in discrete finance model. ASTIN Bulletin. 28/2, 171–186.
7. Embrechts, P., McNeil, A. and Straumann, D. (2002) Correlation and dependency in risk management: properties and pitfalls. In Risk Management: Value at Risk and Beyond, ed. Dempster, M.A.H., Cambridge University Press, Cambridge, pp. 176–233.
8. Frees, E.W. and Valdez, E.A. (1998) Understanding relationships using copulas, North American Actuarial Journal, 2/1, 1–25.
9. Gerber, H.U. (1981) The Esscher premium principle: a criticism Comment, ASTIN Bulletin. 12, 139–140.
10. Gerber, H.U. and Pafumi, G. (1998) Utility functions: from risk theory to finance, North American Actuarial Journal, 2/3, 74–91.
11. Gerber, H.U. and Shiu, E.S.W. (1994) Option pricing by Esscher transforms, Transactions of the Society of Actuaries, XLVI, 99–140.
12. Heilmann, W.R. (1989) Decision theoretic foundations of credibility theory. Insurance: Mathematics and Economics. 8, 77–95.
13. Kamps, U. (1998) On a class of premium principles including the Esscher principle. Scand. Actuarial Journal, 1, 75–80.
14. Kaas, R., Van Heerwaarden, A.E. and Goovaerts, M.J. (1994) Ordering of Actuarial Risks, Caire, Brussels.
15. Meyers, G. (1996) The competitive market equilibrium risk load formula for catastrophe rate-making, Proceedings of the Casualty Actuarial Society, LXXXIII, available from website www.casact.org/pubs/pubs.htm.
16. Mildenhall, S. (2000) Discussion of Michael Wacek's 1997 PCAS Paper – Application of the option market paradigm to the solution of insurance problems, Proceedings of the Casualty Actuarial Society, LXXXVII, available from website www.casact.org/pubs/pubs.htm.
17. Pratt, J.W. (1964) Risk aversion in the small and in the large, Econometrica, 32, 122–136.
18. Taylor, G.C. (1992) Risk exchange I: a unification of some existing results, Scandinavian Actuarial Journal, 15–39.
19. Van Heerwaarden, A.E., Kaas, R. and Goovaerts, M.J. (1989) Properties of the Esscher premium calculation principle, Insurance: Mathematics and Economics. 8, 261–267.
20. Venter, G.G. (1991) Premium implications of reinsurance without arbitrage, ASTIN Bulletin, 21/2, 223–230.
21. Wang, S.S. (1995) Insurance pricing and increased limits ratemaking by proportional hazards transforms, Insurance: Mathematics and Economics, 17, 43–54.
22. Wang, S.S. (1996) Premium calculation by transforming the layer premium density, ASTIN Bulletin, 26/1, 71–92.
23. Wang, S.S. (1998) Aggregation of correlated risks: models and algorithms, Proceedings of the Casualty Actuarial Society, LXXXV, 848–939. It is available from website www.casact.org/pubs/pubs.htm.
24. Wang, S.S. (2000) A class of distortion operators for pricing financial and insurance risks1, Journal of Risk and Insurance, 67/1, 15–36.
25. Wang, S.S. (2002) A universal framework for pricing financial and insurance risks, ASTIN Bulletin, November.
26. Wang, S.S. and Dhane, J. (1998) Comonotonicity, correlation order and premium principles, Insurance Mathematics And Economics, 22/3, 235–242.
27. Wang, S.S., Young, V.R. and Panjer, H.H. (1997) Axiomatic characterization of insurance prices, Insurance: Mathematics and Economics, 21, 173–183.
28. Wirch, J.L. and Hardy, M.R. (1999) A Synthesis of risk measures for capital adequacy, Insurance: Mathematics and Economics, 25/3, 337–347.
29. Zehnwirth, B. (1981) The Esscher premium principle: a criticism, ASTIN Bulletin. 12, 77–78.