Game-Theoretic Capital Asset Pricing in Continuous Time

TL;DR

This paper develops a continuous-time, game-theoretic approach to capital asset pricing, deriving formulas for asset performance without relying on stochastic models or investor preferences, based on an efficient market hypothesis.

Contribution

It introduces a novel game-theoretic framework for CAPM in continuous time, removing stochastic assumptions and investor belief dependencies.

Findings

Derived a CAPM-like formula for expected returns in continuous time

Established that no limited-capacity speculator can outperform the market index substantially

Provided a new perspective on market efficiency without stochastic models

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. This version of the article was essentially written in December 2001 but remains a working paper.