A probability-free and continuous-time explanation of the equity premium and CAPM

TL;DR

This paper introduces a probability-free, continuous-time framework for explaining the equity premium and CAPM, relying solely on positive, continuous price paths without probabilistic assumptions.

Contribution

It provides a novel, probability-free derivation of the equity premium and CAPM in continuous-time financial markets.

Findings

Derived a simple expression for the equity premium

Established a version of the CAPM without probabilistic assumptions

Demonstrated the framework's applicability to idealized markets

Abstract

This paper gives yet another definition of game-theoretic probability in the context of continuous-time idealized financial markets. Without making any probabilistic assumptions (but assuming positive and continuous price paths), we obtain a simple expression for the equity premium and derive a version of the capital asset pricing model.