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Supermodular ordering and stochastic annuities

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  • Goovaerts, Marc
  • Dhaene, Jan

Abstract

In this paper, we consider several types of stochastic annuities, for which an explicit expression of the distribution function is not available. We will construct a random variable with the same mean and which is larger in stop-loss order, for which the distribution function can be easily obtained.

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Bibliographic Info

Paper provided by Katholieke Universiteit Leuven in its series Open Access publications from Katholieke Universiteit Leuven with number urn:hdl:123456789/223220.

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Date of creation: 1999
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Handle: RePEc:ner:leuven:urn:hdl:123456789/223220

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Web page: http://www.kuleuven.be

Related research

Keywords: annuities;

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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. Goovaerts, Marc & Redant, Hendrik, 1999. "On the distribution of IBNR reserves," Insurance: Mathematics and Economics, Elsevier, vol. 25(1), pages 1-9, September.
  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. Hélyette Geman & Marc Yor, 1993. "Bessel Processes, Asian Options, And Perpetuities," Mathematical Finance, Wiley Blackwell, vol. 3(4), pages 349-375.
  5. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
  6. Muller, Alfred, 1997. "Stop-loss order for portfolios of dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 21(3), pages 219-223, December.
  7. Dhaene, Jan & Goovaerts, Marc, 1995. "Dependency of risks and stop-loss order," Open Access publications from Katholieke Universiteit Leuven urn:hdl:123456789/118672, Katholieke Universiteit Leuven.
  8. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
  9. Vanneste, M. & Goovaerts, M. J. & Labie, E., 1994. "The distributions of annuities," Insurance: Mathematics and Economics, Elsevier, vol. 15(1), pages 37-48, October.
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Citations

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Cited by:
  1. Wei, Gang & Hu, Taizhong, 2002. "Supermodular dependence ordering on a class of multivariate copulas," Statistics & Probability Letters, Elsevier, vol. 57(4), pages 375-385, May.
  2. Dhaene, Jan & Denuit, Michel & Goovaerts, Marc & Kaas, R & Vyncke, D, 2002. "The concept of comonotonicity in actuarial science and finance : theory," Open Access publications from Katholieke Universiteit Leuven urn:hdl:123456789/224320, Katholieke Universiteit Leuven.
  3. Vanduffel, S & Dhaene, Jan & Goovaerts, Marc & Kaas, R, 2002. "The hurdle-race problem," Open Access publications from Katholieke Universiteit Leuven urn:hdl:123456789/224324, Katholieke Universiteit Leuven.
  4. Simon, S. & Goovaerts, M. J. & Dhaene, J., 2000. "An easy computable upper bound for the price of an arithmetic Asian option," Insurance: Mathematics and Economics, Elsevier, vol. 26(2-3), pages 175-183, May.
  5. Kaas, R. & Dhaene, Jan & Vyncke, D. & Goovaerts, Marc & Denuit, M., 2002. "A simple geometric proof that comonotonic risks have the convex-largest sum," Open Access publications from Katholieke Universiteit Leuven urn:hdl:123456789/200098, Katholieke Universiteit Leuven.
  6. Frostig, Esther, 2001. "A comparison between homogeneous and heterogeneous portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 29(1), pages 59-71, August.
  7. Cheung, Ka Chun, 2010. "Comonotonic convex upper bound and majorization," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 154-158, October.
  8. Frostig, Esther, 2001. "Comparison of portfolios which depend on multivariate Bernoulli random variables with fixed marginals," Insurance: Mathematics and Economics, Elsevier, vol. 29(3), pages 319-332, December.
  9. Rogers, L. C. G. & Stummer, Wolfgang, 2000. "Consistent fitting of one-factor models to interest rate data," Insurance: Mathematics and Economics, Elsevier, vol. 27(1), pages 45-63, August.

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