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A Benchmark Framework for Risk Management

The paper describes a general framework for contingent claim valuation for finance, insurance and general risk management. It considers security prices and portfolios with finite expected returns, where the growth optimal portfolio is taken as numeraire or benchmark. Benchmarked nonnegative wealth processes are shown to be supermartingales. Fair benchmarked values are conditional expectations of future benchmarked prices under the real world probability measure. Standard risk neutral and actuarial pricing formulas are obtained as special cases of fair pricing. The proposed benchmark framework covers the infinite time horizon and does not require the existence of an equivalent risk neutral pricing measure.

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File URL: http://www.business.uts.edu.au/qfrc/research/research_papers/rp113.pdf
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Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 113.

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Date of creation: 01 Nov 2003
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Handle: RePEc:uts:rpaper:113
Contact details of provider: Postal: PO Box 123, Broadway, NSW 2007, Australia
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Web page: http://www.qfrc.uts.edu.au/

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  1. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
  2. Eckhard Platen & Jason West, 2003. "Fair Pricing of Weather Derivatives," Research Paper Series 106, Quantitative Finance Research Centre, University of Technology, Sydney.
  3. Wolfgang Breymann & Leah Kelly & Eckhard Platen, 2005. "Intraday Empirical Analysis and Modeling of Diversified World Stock Indices," Asia-Pacific Financial Markets, Springer, vol. 12(1), pages 1-28, March.
  4. David Heath & Eckhard Platen, 2003. "Pricing of Index Options Under a Minimal Market Model with Lognormal Scaling," Research Paper Series 101, Quantitative Finance Research Centre, University of Technology, Sydney.
  5. Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney.
  6. David Heath & Eckhard Platen, 2002. "Consistent pricing and hedging for a modified constant elasticity of variance model," Quantitative Finance, Taylor & Francis Journals, vol. 2(6), pages 459-467.
  7. Long, John Jr., 1990. "The numeraire portfolio," Journal of Financial Economics, Elsevier, vol. 26(1), pages 29-69, July.
  8. Eckhard Platen, 2001. "A Minimal Financial Market Model," Research Paper Series 48, Quantitative Finance Research Centre, University of Technology, Sydney.
  9. Hans Buhlmann & Eckhard Platen, 2002. "A Discrete Time Benchmark Approach for Finance and Insurance," Research Paper Series 74, Quantitative Finance Research Centre, University of Technology, Sydney.
  10. 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.
  11. Duffie, Darrell & Huang, Chi-fu, 1986. "Multiperiod security markets with differential information : Martingales and resolution times," Journal of Mathematical Economics, Elsevier, vol. 15(3), pages 283-303, June.
  12. Dirk Becherer, 2001. "The numeraire portfolio for unbounded semimartingales," Finance and Stochastics, Springer, vol. 5(3), pages 327-341.
  13. Eckhard Platen, 2002. "Benchmark Model with Intensity Based Jumps," Research Paper Series 81, Quantitative Finance Research Centre, University of Technology, Sydney.
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