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.
Highlights
In the 1960s, Sharpe (1964), Lintner (1965) and Mossin (1966) established the famous Capital Asset Pricing Model (CAPM for short)
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
Summary
In the 1960s, Sharpe (1964), Lintner (1965) and Mossin (1966) established the famous Capital Asset Pricing Model (CAPM for short). A description of the relationship between the linear evaluation rule and the theory of Markowitz portfolio choice can be found in [2], which they derived a general representation for asset prices that displayed the role of conditioning information. This representation was used to examine restrictions implied by asset pricing models on the unconditional moments of asset payoffs and prices. The fundamental theorem of asset pricing, the portfolio choice of securities and the CAPM all have their continuous-time version.
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