Scandinavian Working Papers in Economics

SSE/EFI Working Paper Series in Economics and Finance,
Stockholm School of Economics

No 122: Diversified Portfolios in Continuous Time

Tomas Björk () and Bertil Näslund ()
Additional contact information
Tomas Björk: Department of Finance, Postal: Stockholm School of Economics, Box 6501, 113 83 Stockholm, Sweden
Bertil Näslund: Department of Finance, Postal: Stockholm School of Economics, Box 6501, 113 83 Stockholm, Sweden

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

JEL-codes: G12; G13

28 pages, September 1996

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