Actuarial risk measures for financial derivative pricing

Insurance: Mathematics and Economics

Volumn 42, Issue 2, 2008, Pages 540-547

  Goovaerts, Marc J ^a,b   Laeven, Roger J A ^a  

^a UNIVERSITY OF AMSTERDAM   (Netherlands)

^b UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

Comonotonicity; Derivative pricing; Equivalent martingale measure; Esscher transform; Feynman Kac integration; Girsanov's theorem; Incomplete markets; Stochastic ordering

Indexed keywords

EID: 40949100441     PISSN: 01676687     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.insmatheco.2007.04.001     Document Type: Article

References (29)

1. Borch K. Equilibrium in a reinsurance market. Econometrica 3 (1962) 424-444
2. Bühlmann H. An economic premium principle. Astin Bulletin 11 (1980) 52-60
3. Bühlmann H. Premium calculation from top down. Astin Bulletin 15 (1985) 89-101
4. Bühlmann H., Delbaen F., Embrechts P., and Shiryaev A.N. No-arbitrage, change of measure and conditional Esscher transforms. CWI Quarterly 9 (1996) 291-317
5. Cox J., and Ross S. The valuation of options for alternative stochastic processes. Journal of Financial Economics 3 (1976) 145-166
6. Denneberg D. Non-Additive Measure and Integral (1994), Kluwer Academic Publishers, Boston
7. Denuit M. Laplace transform ordering of actuarial quantities. Insurance: Mathematics and Economics 29 (2001) 83-102
8. Denuit M., Dhaene J., Goovaerts M.J., Kaas R., and Laeven R.J.A. Risk measurement with equivalent utility principles. In: Rüschendorf L. (Ed). Risk Measures: General Aspects and Applications. Statistics and Decisions 24 (2006) 1-26 (special issue)
9. Duffie D. Dynamic Asset Pricing Theory. 2nd edn (1996), Princeton University Press, Princeton
10. Embrechts P. Actuarial versus financial pricing of insurance. Risk Finance 1 (2000) 17-26
11. Esscher F. On the probability function in the collective theory of risk. Scandinavian Actuarial Journal 15 (1932) 175-195
12. Feynman R.P., and Hibbs A.R. Quantum Mechanics and Path Integrals (1965), McGraw-Hill, New York
13. Gerber H.U. An Introduction to Mathematical Risk Theory. Huebner Foundation Monograph vol. 8 (1979), Homewood, Illinois
14. Gerber H.U., and Goovaerts M.J. On the representation of additive principles of premium calculation. Scandinavian Actuarial Journal 4 (1981) 221-227
15. Gerber H.U. The Esscher premium principle: A criticism, comment. Astin Bulletin 12 (1981) 139-140
16. Gerber H.U., and Shiu E.S.W. Option pricing by Esscher transforms. Transactions of the Society of Actuaries 46 (1994) 99-191
17. Gerber H.U., and Shiu E.S.W. Actuarial bridges to dynamic hedging and option pricing. Insurance: Mathematics and Economics 18 (1996) 183-218
18. Goovaerts M.J., De Vylder F.E.C., and Haezendonck J. Insurance Premiums (1984), North Holland Publishing, Amsterdam
19. Goovaerts M.J., Kaas R., Laeven R.J.A., and Tang Q. A comonotonic image of independence for additive risk measures. Insurance: Mathematics and Economics 35 (2004) 581-594
20. Hadar J., and Russell W.R. Rules for ordering uncertain prospects. American Economic Review 59 (1969) 25-34
21. Harrison J.M., and Kreps D.M. Martingales and arbitrage in multiperiod securities markets. Journal of Economic Theory 20 (1979) 381-408
22. Harrison J.M., and Pliska S.R. Martingales and stochastic integrals in the theory of continuous trading. Stochastic Processes and their Applications 11 (1981) 215-260
23. Iwaki H., Kijima M., and Morimoto Y. An economic premium principle in a multiperiod economy. Insurance: Mathematics and Economics 28 (2001) 325-339
24. Karatzas I., and Shreve S.E. Brownian Motion and Stochastic Calculus (1988), Springer-Verlag, New York
25. Laeven, Roger J.A., 2005. Essays on risk measures and stochastic dependence. Tinbergen Institute Research Series 360. Thela Thesis. Amsterdam
26. Laeven, Roger J.A., Goovaerts, Marc J., 2007. Premium calculation and insurance pricing. In: Encyclopedia of Quantitative Risk Assessment. Wiley (in press)
27. Rothschild M., and Stiglitz J.E. Increasing risk I: A definition. Journal of Economic Theory 2 (1970) 225-243
28. Savage L.J. The Foundations of Statistics (1954), Wiley, New York
29. Wang S.S. Equilibrium pricing transforms: New results using Bühlmann's 1980 economic model. Astin Bulletin 33 (2003) 57-73