Knowledge representation and integration for portfolio evaluation using linear belief functions

Abstract

In this paper, we propose a linear belief function approach to evaluating portfolio performance. By drawing on the notion of linear belief functions, we propose an elementary approach to knowledge representation for expert systems using linear belief functions. We show 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. We 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 information. We use an example of three gold stocks to illustrate the approach.