Diversified Portfolios in Continuous Time

Working Paper No. 122

Posted: 12 Feb 1997

See all articles by Tomas Bjork

Tomas Bjork

Stockholm School of Economics - Swedish House of Finance

Bertil Näslund

Stockholm School of Economics - Department of Finance

Date Written: September 1996

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) 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

Bjork, Tomas and Näslund, Bertil, Diversified Portfolios in Continuous Time (September 1996). Working Paper No. 122. Available at SSRN: https://ssrn.com/abstract=2299

Tomas Bjork (Contact Author)

Stockholm School of Economics - Swedish House of Finance ( email )

Drottninggatan 98
111 60 Stockholm
Sweden

Bertil Näslund

Stockholm School of Economics - Department of Finance ( email )

SE-113 83 Stockholm
Sweden
+46-8-736 91 41 (Phone)
+46-8-31 23 27 (Fax)

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