A subjective assessment of approximate probabilities with a portfolio application

This paper extends the assessment of approximate probabilities in two important directions. The first is to investigate some mathematical relations between the probability ranges and derives the most unbiased probability for the case when the limits are subjectively defined. The second is to suggest a simple method to determine the optimal solution which represents the optimal portfolio proportions of securities that possess the minimum risk measured by the maximum entropy measure. The paper considers the derivation of portfolio modeling under a fuzzy situation using probability theory, and provides various other (non-probabilistic) scenarios with their utility in risk modeling. A simple method for identification of mean-entropic frontier is proposed. Then, a comparison of mean-variance procedure with the discrete mean-entropic method is implemented by an example.