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The concept of comonotonicity in actuarial science and finance: applications

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  • Dhaene, J.
  • Denuit, M.
  • Goovaerts, M. J.
  • Kaas, R.
  • Vyncke, D.

Abstract

In an insurance context, one is often interested in the distribution function of a sum of random variables. Such a sum appears when considering the aggregate claims of an insurance portfolio over a certain reference period. It also appears when considering discounted payments related to a single policy or a portfolio at different future points in time. The assumption of mutual independence between the components of the sum is very convenient from a computational point of view, but sometimes not realistic. In Dhaene, Denuit, Goovaerts, Kaas, Vyncke (2001), we determined approximations for sums of random variables, when the distributions of the components are known, but the stochastic dependence structure between them is unknown or too cumbersome to work with. Practical applications of this theory will be considered in this paper. Both papers are to a large extent an overview of recent research results obtained by the authors, but also new theoretical and practical results are presented.

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Bibliographic Info

Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

Volume (Year): 31 (2002)
Issue (Month): 2 (October)
Pages: 133-161

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Handle: RePEc:eee:insuma:v:31:y:2002:i:2:p:133-161

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Web page: http://www.elsevier.com/locate/inca/505554

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References

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  1. De Schepper, A. & Teunen, M. & Goovaerts, M., 1994. "An analytical inversion of a Laplace transform related to annuities certain," Insurance: Mathematics and Economics, Elsevier, vol. 14(1), pages 33-37, April.
  2. Gerber, Hans U. & Shiu, Elias S. W., 1996. "Actuarial bridges to dynamic hedging and option pricing," Insurance: Mathematics and Economics, Elsevier, vol. 18(3), pages 183-218, November.
  3. Milevsky, Moshe Arye, 1997. "The present value of a stochastic perpetuity and the Gamma distribution," Insurance: Mathematics and Economics, Elsevier, vol. 20(3), pages 243-250, October.
  4. Kemna, A. G. Z. & Vorst, A. C. F., 1990. "A pricing method for options based on average asset values," Journal of Banking & Finance, Elsevier, vol. 14(1), pages 113-129, March.
  5. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
  6. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
  7. Kaas, R & Dhaene, Jan & Goovaerts, Marc, 2000. "Upper and lower bounds for sums of random variables," Open Access publications from Katholieke Universiteit Leuven urn:hdl:123456789/223713, Katholieke Universiteit Leuven.
  8. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: theory," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 3-33, August.
  9. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  10. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
  11. Goovaerts, Marc & Dhaene, Jan & De Schepper, A, 1999. "Stochastic upper bounds for present value functions," Open Access publications from Katholieke Universiteit Leuven urn:hdl:123456789/118656, Katholieke Universiteit Leuven.
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