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Diversified Portfolios with Jumps in a Benchmark Framework

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Abstract

This paper considers diversifed portfolios in a sequence of jump diffusion market models. Conditions for the approximation of the growth optimal portfolio (GOP) by diversified portfolios are provided. Under realistic assumptions, it is shown that diversified portfolios approximate the GOP without requiring any major model specifications. This provides a basis for systematic use of diversified stock indices as proxies for the GOP in derivative pricing, risk management and portfolio optimization.

Suggested Citation

  • Eckhard Platen, 2004. "Diversified Portfolios with Jumps in a Benchmark Framework," Research Paper Series 129, Quantitative Finance Research Centre, University of Technology, Sydney.
    • Handle: RePEc:uts:rpaper:129
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    File URL: http://www.qfrc.uts.edu.au/research/research_papers/rp129.pdf
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    1. Wolfgang Breymann & Leah Kelly & Eckhard Platen, 2005. "Intraday Empirical Analysis and Modeling of Diversified World Stock Indices," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 12(1), pages 1-28, March.
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    4. Eckhard Platen, 2004. "A Benchmark Framework for Risk Management," World Scientific Book Chapters, in: Jiro Akahori & Shigeyoshi Ogawa & Shinzo Watanabe (ed.), Stochastic Processes And Applications To Mathematical Finance, chapter 15, pages 305-335, World Scientific Publishing Co. Pte. Ltd..
    5. Tomas Björk & Bertil Näslund, 1998. "Diversified Portfolios in Continuous Time," Review of Finance, European Finance Association, vol. 1(3), pages 361-387.
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    8. Eckhard Platen, 2004. "Modeling The Volatility And Expected Value Of A Diversified World Index," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 7(04), pages 511-529.
    9. 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.
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    13. Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney.
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    15. 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.
    16. Leah Kelly, 2004. "Inference and Intraday Analysis of Diversified World Stock Indices," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2004.
    17. 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.
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    22. 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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    More about this item

    Keywords

    benchmark model; growth optimal portfolio; diversified portfolio;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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