دانلود رایگان مقاله چارچوب احتمال برای مدل تصمیم گیری عوامل اقتصادی، تحت عدم قطعیت

Abstract

The applications of techniques from statistical (and classical) mechanics to model interesting problems in economics and finance have produced valuable results. The principal movement which has steered this research direction is known under the name of ‘econophysics’. In this paper, we illustrate and advance some of the findings that have been obtained by applying the mathematical formalism of quantum mechanics to model human decision making under ‘uncertainty’ in behavioral economics and finance. Starting from Ellsberg's seminal article, decision making situations have been experimentally verified where the application of Kolmogorovian probability in the formulation of expected utility is problematic. Those probability measures which by necessity must situate themselves in Hilbert space (such as ‘quantum probability’) enable a faithful representation of experimental data. We thus provide an explanation for the effectiveness of the mathematical framework of quantum mechanics in the modeling of human decision making. We want to be explicit though that we are not claiming that decision making has microscopic quantum mechanical features.

4. Quantum structures in the Ellsberg paradox We expose in this section our approach to economic agents decision making based on the mathematical formalism of quantum mechanics. We do not present the technical details of our modeling, but instead we aim to be as intuitive and explicative as possible. The reader interested to the technical aspects of our approach can refer to our papers (Aerts et al., 2014), (Khrennikov & Haven, 2009), (Aerts et al., 2012). The first insight towards the elaboration of a quantum probabilistic framework to model Ellsberg-type situations came from our conceptual and structural investigation of how the approaches generalizing SEUT cope with ambiguity and ambiguity aversion (Gilboa, 1987), (Gilboa & Schmeidler, 1989), (Maccheroni et al., 2006), (Klibanoff et al., 2005). As we know, ambiguity characterizes a situation without a probability model describing it, while risk characterizes a situation where one presupposes that a classical probability model on a σ–algebra of events exists. The generalizations in (i)–(iv), Section 3, consider more general structures than a single classical probability model on a σ–algebra. We are convinced that this is exactly the point: ambiguity, due to its contextual nature, structurally needs a non-classical probability model. To this end we have elaborated a general framework for this type of situations, based on the notion of ‘contextual risk’ and inspired by the probability structure of quantum mechanics. The latter is indeed intrinsically different from a classical probability on a σ–algebra, because the set of events does ‘not’ form a Boolean algebra (see Section 2).