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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 380718, 9 pages
http://dx.doi.org/10.1155/2014/380718
Research Article

Pricing of Equity Indexed Annuity under Fractional Brownian Motion Model

1School of Mathematics and Computer Science, Anhui Normal University, Wuhu, Anhui 241002, China
2School of Finance, Nanjing University of Finance and Economics, Nanjing, Jiangsu 210046, China

Received 13 December 2013; Revised 16 March 2014; Accepted 21 March 2014; Published 24 April 2014

Academic Editor: Yiming Ding

Copyright © 2014 Lin Xu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. Marrion, “4th quarter index annuity sales,” 2007, http://www.indexannuity.org.
  2. S. Tiong, “Valuing equity-indexed annuities,” North American Actuarial Journal, vol. 4, no. 4, pp. 149–163, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. P. Boyle and W. Tian, “The design of equity-indexed annuities,” Insurance: Mathematics & Economics, vol. 43, no. 3, pp. 303–315, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. H. U. Gerber and E. S. W. Shiu, “Pricing lookback options and dynamic guarantees,” North American Actuarial Journal, vol. 7, no. 1, pp. 48–67, 2003, With discussion by Griselda Deelstra. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. M. Hardy, Investment Guarantees: Modeling and Risk Management for Equity-Linked Life Insurance, John Wiley & Sons, Ontario, Canada, 2003.
  6. S. Jaimungal, “Pricing and hedging equity indexed annuities with variance gamma deviates,” 2004, http://www.utstat.utoronto.ca/sjaimung/papers/eiaVG.pdf.
  7. M. Kijima and T. Wong, “Pricing of ratchet equity-indexed annuities under stochastic interest rates,” Insurance: Mathematics & Economics, vol. 41, no. 3, pp. 317–338, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. H. Lee, “Pricing equity-indexed annuities with path-dependent options,” Insurance: Mathematics & Economics, vol. 33, no. 3, pp. 677–690, 2003. View at Publisher · View at Google Scholar · View at Scopus
  9. X. S. Lin and K. S. Tan, “Valuation of equity-indexed annuities under stochastic interest rates,” North American Actuarial Journal, vol. 7, no. 4, pp. 72–91, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. K. S. Moore, “Optimal surrender strategies for equity-indexed annuity investors,” Insurance: Mathematics & Economics, vol. 44, no. 1, pp. 1–18, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. E. Biffis, “Affine processes for dynamic mortality and actuarial valuations,” Insurance: Mathematics & Economics, vol. 37, no. 3, pp. 443–468, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. E. Biffis, M. Denuit, and P. Devolder, “Stochastic mortality under measure changes,” Cass Business School Research Paper, 2005.
  13. D. Hainaut and P. Devolder, “Mortality modelling with Lévy processes,” Insurance: Mathematics & Economics, vol. 42, no. 1, pp. 409–418, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. L. Jalen and R. Mamon, “Valuation of contingent claims with mortality and interest rate risks,” Mathematical and Computer Modelling, vol. 49, no. 9-10, pp. 1893–1904, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. L. Qian, W. Wang, R. Wang, and Y. Tang, “Valuation of equity-indexed annuity under stochastic mortality and interest rate,” Insurance: Mathematics & Economics, vol. 47, no. 2, pp. 123–129, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. Y. Aít-Sahalia, “Nonparametric pricing of interest rate derivative securities,” Econometrica, vol. 64, no. 3, pp. 527–560, 1996. View at Google Scholar · View at Scopus
  17. L. Andrew, “Long-term memory in stock price,” Econometrica, vol. 59, pp. 1279–1313, 1991. View at Google Scholar
  18. C. W. J. Granger, “A typical spectral shape of an economic variable,” Econometrica, vol. 34, pp. 150–161, 1966. View at Google Scholar
  19. T. Sottinen and E. Valkeila, “Fractional Brownain motion as a model in finance,” Report, http://www.mathstat.helsinki.fi/reports/Preprint302.ps.
  20. W. Willinger, M. Taqqu, and V. Teverovsky, “Stock market prices and long-range dependence,” Finance and Stochastics, vol. 3, pp. 1–13, 1999. View at Google Scholar
  21. R. Dudley and R. Norvaisa, An Introduction to P-Variation and Young Integrals with Emphasis on Sample Functions of Stochastic Processes, MaPhySto, Department of Mathematical Sciences, University of Aarhus, 1998.
  22. T. E. Duncan, Y. Hu, and B. Pasik-Duncan, “Stochastic calculus for fractional Brownian motion. I. Theory,” SIAM Journal on Control and Optimization, vol. 38, no. 2, pp. 582–612, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. Y. Hu and B. Øksendal, “Fractional white noise calculus and applications to finance,” Infinite Dimensional Analysis, Quantum Probability and Related Topics, vol. 6, no. 1, pp. 1–32, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. I. Norros, E. Valkeila, and J. Virtamo, “An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motions,” Bernoulli, vol. 5, no. 4, pp. 571–587, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. R. A. Jarrow, P. Protter, and H. Sayit, “No arbitrage without semimartingales,” The Annals of Applied Probability, vol. 19, no. 2, pp. 596–616, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. H. M. Soner, S. E. Shreve, and J. Cvitanić, “There is no nontrivial hedging portfolio for option pricing with transaction costs,” The Annals of Applied Probability, vol. 5, no. 2, pp. 327–355, 1995. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. O. Narayan, “Exact asymptotic queue length distribution for fractional Brownian traffic,” Advances in Performance Analysis, vol. 1, pp. 39–63, 1998. View at Google Scholar
  28. Z. Michna, “Self-similar processes in collective risk theory,” Journal of Applied Mathematics and Stochastic Analysis, vol. 11, no. 4, pp. 429–448, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  29. B. Ferebee, “An asymptotic expansion for one-sided Brownian exit densities,” Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol. 63, no. 1, pp. 1–15, 1983. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  30. S. Asmussen, Ruin Probabilities, World Scientific Publishing, Singapore, 2000. View at MathSciNet