Projective Capital Asset Pricing Model

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This paper is interested in exploring the capabilities and limitations of investment decision making under uncertainty through the lens of Quantum Probabilities/formalism stand and will be focusing on the Capital Asset Pricing Model as use case. Our main purpose is to examine the historical and structural foundations surrounding decision making paradoxes. To ease the comprehension of the issue to the common reader, we first outline key cornerstones of investment decision making under the two competing conceptual frameworks, expected utility and mean-variance. We review then the axiomatic justifications of the mean-variance and set the comparison with the Expected utility generally. That's when the analogy with quantum probabilities arises. This comes from the fact that decision making process seems to be more likely to be presented in terms of amplitudes. Thus, here the quantum probabilities refer to a calculus of quantum states and not of probabilities. In the final section, we present the capital asset pricing model to understand the appeal of the usage of Mean variance over Expected utility in the financial theory, and how we can remediate to this approach once decisions are depicted in terms of quantum probability amplitudes. Several extensions of the rational decision-making theory using classical probability formulations emerged depending on the actual empirical findings, trying to explain such paradoxes and improve the existing framework decision making theory. These simplifying assumptions were seeking to generate the probabilistic measures assumptions without linearity or to make State-independent probabilistic estimates as well as agents’ possessing firm assumptions in the generalized utility theory loosened. While these trials helped to discuss the pitfalls of the classical probabilities in some decision-making situations, it failed to give a harmonized expected utility theoretical model. An established theory to consider is the prospect theory by Kahneman and Tversky which encompasses the human biases and heuristic. Indeed, its attributes make this theory likely to be extended to a general framework of the decision-making theory by using quantum probabilities as the mathematical scope.


Decision Making, mean–variance, expected utility, Decision Making paradoxes, Borsch’s paradox, quantum probability, probability mixture, portfolio theory, CAPM

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IDR: 14124345   |   DOI: 10.47813/2782-2818-2022-2-4-0201-0213