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

DOI: 10.4236/jmf.2012.24034, PP. 315-320

Keywords: Fractional Brownian Motion, Clark-Haussmann-Ocone Theorem, Fractional Girsanov Theorem, Evaluation Operator, Capital Asset Pricing Model

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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.

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