Knowledge representation and integration for portfolio evaluation using linear belief functions

This paper proposes a linear belief function (LBF) approach to evaluate portfolio performance. By drawing on the notion of LBFs, an elementary approach to knowledge representation in expert systems is proposed. It is shown how to use basic matrices to represent market information and financial knowledge, including complete ignorance, statistical observations, subjective speculations, distributional assumptions, linear relations, and empirical asset-pricing models. The authors then appeal to Dempster's rule of combination to integrate the knowledge for assessing the overall belief of portfolio performance and updating the belief by incorporating additional evidence. An example of three gold stocks is used to illustrate the approach.