Fractional order entropy-based decision-making models under risk

Abstract: The construction of an efficient portfolio with a good level of return and minimal risk depends on selecting the optimal combination of stocks. This paper introduces a novel decision-making framework for stock selection based on fractional order entropy due to Ubriaco. By tuning the fractional parameter, the model captures varying attitudes of individuals toward risk. Values of fractional parameter near one indicate high risk tolerance (adventurous attitude), while those near zero reflect risk aversion (conservative attitude). The sensitivity of the fractional order entropy to changing risk preferences of decision makers is demonstrated through four real world portfolio models, namely, large cap, mid cap, diversified, and hypothetical. Furthermore, two new risk measures, termed as expected utility fractional entropy (EU FE) and expected utility fractional entropy and variance (EU FEV), are introduced to develop decision models aligned with investors risk preferences. The effectiveness of the decision model is further tested with financial stock market data of PSI index by finding efficient frontiers of portfolio with the aid of artificial neural network.