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Diversified Portfolios in Continuous Time

  • Björk, Tomas

    ()

    (Department of Finance)

  • Näslund, Bertil

    ()

    (Department of Finance)

We study a financial market containing an infinite number of assets, where each asset price is driven by an idiosyncratic random source as well as by a systematic noise term. Introducing 2 asymptotic assets" which correspond to certain infinitely well diversified portfolios we study absence of (asymptotic) arbiytrage, and in this context we obtain continuous time extensions of atemporal APT results. We also study completeness and derivative pricing, showing that the possibility of forming infinitely well diversified portfolios has the property of completing the market. It also turns out that models where the all risk is of diffusion type are qualitatively quite different from models where one risk is of diffusion type and the other is of Poisson type. We also present a simple martingale based theory for absence of asymptotic arbitrage.

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Paper provided by Stockholm School of Economics in its series SSE/EFI Working Paper Series in Economics and Finance with number 122.

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Length: 28 pages
Date of creation: Sep 1996
Date of revision:
Publication status: Published in European Finance Review, 1998, pages 361-387.
Handle: RePEc:hhs:hastef:0122
Contact details of provider: Postal: The Economic Research Institute, Stockholm School of Economics, P.O. Box 6501, 113 83 Stockholm, Sweden
Phone: +46-(0)8-736 90 00
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Web page: http://www.hhs.se/
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  1. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
  2. Tomas Björk & Yuri Kabanov & Wolfgang Runggaldier, 1997. "Bond Market Structure in the Presence of Marked Point Processes," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 211-239.
  3. Huberman, Gur, 1982. "A simple approach to arbitrage pricing theory," Journal of Economic Theory, Elsevier, vol. 28(1), pages 183-191, October.
  4. Reisman, Haim, 1992. "Intertemporal Arbitrage Pricing Theory," Review of Financial Studies, Society for Financial Studies, vol. 5(1), pages 105-22.
  5. Y.M. Kabanov & D.O. Kramkov, 1998. "Asymptotic arbitrage in large financial markets," Finance and Stochastics, Springer, vol. 2(2), pages 143-172.
  6. Chamberlain, Gary, 1988. "Asset Pricing in Multiperiod Securities Markets," Econometrica, Econometric Society, vol. 56(6), pages 1283-1300, November.
  7. Chen, Nai-Fu & Roll, Richard & Ross, Stephen A, 1986. "Economic Forces and the Stock Market," The Journal of Business, University of Chicago Press, vol. 59(3), pages 383-403, July.
  8. Jarrow, Robert A & Turnbull, Stuart M, 1995. " Pricing Derivatives on Financial Securities Subject to Credit Risk," Journal of Finance, American Finance Association, vol. 50(1), pages 53-85, March.
  9. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-87, September.
  10. Philippe Artzner & Freddy Delbaen, 1995. "Default Risk Insurance And Incomplete Markets," Mathematical Finance, Wiley Blackwell, vol. 5(3), pages 187-195.
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