The market information filtration asset pricing model

The information-based approach asset pricing model by Brody-Hughston-Macrina is constructed based on the dividends information that can be accessed by investors at recent time in a financial market. Brody-Hughston-Macrina modeled the asset pricing at recent time for case of the cash flows value paying a single dividend at the certain time. The model is given by the expectation of the upcoming dividends conditional at the market information filtration under the risk neutral probability measure. The market information filtration is contained by the recent information flows that represent sum of the two of information i.e. the true information of dividends and the noise information in the financial market. Brody-Hughston-Macrina also constructed a model from setting that is a limited-liability asset that pays no interim dividends and is sold off at time fixed for the certain value. In this model, the recent information flows represent the sum of the market factor information and the noise information. Then this model is called a Black-Scholes Model from an Information-Based Perspective. Brody-Hughston-Macrina did imprecision in using of Gaussian Integrals to obtain the final result of the Black-Scholes Model from an Information-Based Perspective. This paper explains an imprecision for using of Gaussian Integrals in deriving the final result of the Black-Sholes Model from an Informative-Perspective, so it is found a different final model from the final model by Brody-Hughston-Macrina.