Game-Theoretic Capital Asset Pricing in Continuous Time

Vovk, Vladimir; Shafer, Glenn

doi:10.2139/ssrn.303062

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Game-Theoretic Capital Asset Pricing in Continuous Time

Game-Theoretic Probability Project Working Paper No. 2

12 Pages Posted: 13 Mar 2002

See all articles by Vladimir Vovk

Vladimir Vovk

Royal Holloway, University of London; Royal Holloway, University of London

Glenn Shafer

Rutgers, The State University of New Jersey - Accounting & Information Systems

Date Written: December 30, 2001

Abstract

We derive formulas for the performance of capital assets in continuous time from an efficient market hypothesis, with no stochastic assumptions and no assumptions about the beliefs or preferences of investors. Our efficient market hypothesis says that a speculator with limited means cannot beat a particular index by a substantial factor. Our results include a formula that resembles the classical CAPM formula for the expected simple return of a security or portfolio.

Keywords: CAPM, Capital Asset Pricing Model, EMH, Efficient Market Hypothesis, continuous time, non-standard analysis, performance deficit, portfolio performance, performance of mutual funds

JEL Classification: G12, G14, G11, C12

Suggested Citation: Suggested Citation

Vovk, Vladimir and Vovk, Vladimir and Shafer, Glenn, Game-Theoretic Capital Asset Pricing in Continuous Time (December 30, 2001). Game-Theoretic Probability Project Working Paper No. 2, Available at SSRN: https://ssrn.com/abstract=303062 or http://dx.doi.org/10.2139/ssrn.303062