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The Economic Research Institute, Stockholm School of Economics SSE/EFI Working Paper Series in Economics and Finance

No 122:
Diversified Portfolios in Continuous Time

Tomas Björk () and 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 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.

Keywords: Large economies; diversifiable risk; APT; asymptotic arbitrage; completeness; martingales; (follow links to similar papers)

JEL-Codes: G12; G13; (follow links to similar papers)

28 pages, September 1996

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This paper is published as:
Björk, Tomas and Bertil Näslund, (1998), 'Diversified Portfolios in Continuous Time', European Finance Review, Vol. 1, No. 3, pages 361-387



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