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A Discrete Time Benchmark Approach for Finance and Insurance

This paper proposes an integrated appraoch to discrete time modelling in finance and insurance. This approach is based on the existence of a specific benchmark portfolio, known as the growth optimal portfolio. When used as numeraire, this portfolio ensures that all benchmarked price processes are super-martingales. A fair market is characterized in terms of the type of maximum that the optimal growth rate attains. In general, arbitrage amounts arise due to supermartingale property of benchmarked traded prices. No measure transformation is needed for the pricing of insurance policies and derivatives in a fair market.

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File URL: http://www.business.uts.edu.au/qfrc/research/research_papers/rp74.pdf
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Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 74.

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Date of creation: 01 Mar 2002
Date of revision:
Handle: RePEc:uts:rpaper:74
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Web page: http://www.qfrc.uts.edu.au/

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  1. Constantinides, George M, 1992. "A Theory of the Nominal Term Structure of Interest Rates," Review of Financial Studies, Society for Financial Studies, vol. 5(4), pages 531-52.
  2. Long, John Jr., 1990. "The numeraire portfolio," Journal of Financial Economics, Elsevier, vol. 26(1), pages 29-69, July.
  3. Eckhard Platen, 2001. "A Minimal Financial Market Model," Research Paper Series 48, Quantitative Finance Research Centre, University of Technology, Sydney.
  4. I. Bajeux-Besnainou & R. Portait, 1997. "The numeraire portfolio: a new perspective on financial theory," The European Journal of Finance, Taylor & Francis Journals, vol. 3(4), pages 291-309.
  5. N. Hofmann & E. Platen & M. Schweizer, 1992. "Option Pricing under Incompleteness and Stochastic Volatility," Discussion Paper Serie B 209, University of Bonn, Germany.
  6. L. C. G. Rogers, 1997. "The Potential Approach to the Term Structure of Interest Rates and Foreign Exchange Rates," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 157-176.
  7. 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.
  8. 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.
  9. Buhlmann, H., 1992. "Stochastic discounting," Insurance: Mathematics and Economics, Elsevier, vol. 11(2), pages 113-127, August.
  10. Dirk Becherer, 2001. "The numeraire portfolio for unbounded semimartingales," Finance and Stochastics, Springer, vol. 5(3), pages 327-341.
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