TITLE:
From Dynamic Linear Evaluation Rule to Dynamic CAPM in a Fractional Brownian Motion Environment
AUTHORS:
Qing Zhou, Chao Li
KEYWORDS:
Fractional Brownian Motion; Clark-Haussmann-Ocone Theorem; Fractional Girsanov Theorem; Evaluation Operator; Capital Asset Pricing Model
JOURNAL NAME:
Journal of Mathematical Finance,
Vol.2 No.4,
November
23,
2012
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.