Quantum Uncertainty in Decision Theory

Vyacheslav I. Yukalov

Vyacheslav I. Yukalov, Didier Sornette

Lizhi Xin, Houwen Xin

Keano De Vos, Gert de Cooman, Alexander Erreygers +1 more

Ana Njegovanović

In this paper we present several questions: can we use quantum theory in financial decision making? Is there a way that quantum theory influences financial decision-making in terms of risk and uncertainty? What are the relations of quantum theory of decision-making and the role of prefrontal cortex and emotion in the conditions of risk and uncertainty? Perhaps there are already answers to these questions, perhaps they are already answered or need further research and development in the participation of financial decision-making in the conditions of risk and uncertainty in quantum theory of decision-making. Expanding on the role of prefrontal cortex and emotion work seeks to provide a consistent and integrated view of the complexity of financial decision-making in the conditions of risk and uncertainty. This study combines various scientific disciplines, concepts and mathematical (classical financial mathematics-based on the theory of stochastic processes) of the financial decision-making structure in terms of risk and uncertainty. One of the key factors in making financial decisions that lead to quantum dynamics is risk, uncertainty and emotion. The quantum decision theory were developed based on the mathematical techniques of complex Hilbert spaces through composite perspective lattices. Quantum decisional theory analyzes the decision-making process and types of dynamic inconsistency, quantum approaches to decision-making in the conditions of risk and uncertainty, taking Allais paradox and reinterpretation not on the subject's side but on the side of the observer (Allais paradox concerning the quantum measurement problem and the effect of the observer). Relationships between financial decision-making in risk and uncertainty and prefrontal cortex (frontal, cingulate parietal cortex, and striatum and emotion) show the motives of rational / irrational financial decision-making. Financial decision-making explains theoretical foundations (from the aspect of traditional economy) while neuroscience considers physiological aspects and somatic variables that influence financial decision-making.

Vyacheslav I. Yukalov, Didier Sornette

Theory of quantum measurements is often classified as decision theory. An event in decision theory corresponds to the measurement of an observable. This analogy looks clear for operationally testable simple events. However, the situation is essentially more complicated in the case of composite events. The most difficult point is the relation between decisions under uncertainty and measurements under uncertainty. We suggest a unified language for describing the processes of quantum decision making and quantum measurements. The notion of quantum measurements under uncertainty is introduced. We show that the correct mathematical foundation for the theory of measurements under uncertainty, as well as for quantum decision theory dealing with uncertain events, requires the use of positive operator-valued measure that is a generalization of projection-valued measure. The latter is appropriate for operationally testable events, while the former is necessary for characterizing operationally uncertain events. In both decision making and quantum measurements, one has to distinguish composite nonentangled events from composite entangled events. Quantum probability can be essentially different from classical probability only for entangled events. The necessary condition for the appearance of an interference term in the quantum probability is the occurrence of entangled prospects and the existence of an entangled strategic state of a decision maker or of an entangled statistical state of a measuring device.