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Diversified Portfolios in Continuous Time

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  • Tomas Björk
  • Bertil Näslund

Abstract

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 "asymptotic assets" which correspond to certain infinitely well diversified portfolios we study absence of (asymptotic) arbitrage, 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. JEL Classification: G12, G13,

Suggested Citation

  • Tomas Björk & Bertil Näslund, 1998. "Diversified Portfolios in Continuous Time," Review of Finance, European Finance Association, vol. 1(3), pages 361-387.
    • Handle: RePEc:oup:revfin:v:1:y:1998:i:3:p:361-387.
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    File URL: http://hdl.handle.net/10.1023/A:1009707929295
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    References listed on IDEAS

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    Cited by:

    1. Eckhard Platen, 2004. "Diversified Portfolios with Jumps in a Benchmark Framework," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(1), pages 1-22, March.
    2. Erdinc Akyildirim & Frank J. Fabozzi & Ahmet Goncu & Ahmet Sensoy, 2022. "Statistical arbitrage in jump-diffusion models with compound Poisson processes," Annals of Operations Research, Springer, vol. 313(2), pages 1357-1371, June.
    3. Lim Kian Guan & Liu Xiaoqing & Tsui Kai Chong, 2004. "Asymptotic dynamics and value-at-risk of large diversified portfolios in a jump-diffusion market," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 129-139.

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    More about this item

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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