From Dynamic Linear Evaluation Rule to Dynamic CAPM in a Fractional Brownian Motion Environment

Qing Zhou, Chao Li

School of Science, Beijing University of Posts and Telecommunications, Beijing, China.

DOI: 10.4236/jmf.2012.24034                

Abstract

In this paper, we present the fundamental framework of the evaluation problem under which the evaluation operator satisfying some axioms is linear. Based on the dynamic linear evaluation mechanism of contingent claims, studying this evaluation rule in the market driven by fractional Brownian motions has led to a dynamic capital asset pricing model. It is deduced here mainly with the fractional Girsanov theorem and the Clark-Haussmann-Ocone theorem.

Keywords

Fractional Brownian Motion; Clark-Haussmann-Ocone Theorem; Fractional Girsanov Theorem; Evaluation Operator; Capital Asset Pricing Model

Conflicts of Interest

The authors declare no conflicts of interest.

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