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Unformatted text preview: Physics of risk and uncertainty in quantum decision making V.I. Yukalov 1 , 2 ,a and D. Sornette 1 , 3 ,b 1 Department of Management, Technology and Economics, Swiss Federal Institute of Technology, ETH Zurich, Kreuzplatz 5, Zurich 8032, Switzerland 2 Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, Russia 3 Swiss Finance Institute, University of Geneva, CH-1211 Geneva 4, Switzerland Abstract The Quantum Decision Theory, developed recently by the authors, is applied to clarify the role of risk and uncertainty in decision making and in particular in relation to the phe- nomenon of dynamic inconsistency. By formulating this notion in precise mathematical terms, we distinguish three types of inconsistency: time inconsistency, planning para- dox, and inconsistency occurring in some discounting effects. While time inconsistency is well accounted for in classical decision theory, the planning paradox is in contradiction with classical utility theory. It finds a natural explanation in the frame of the Quan- tum Decision Theory. Different types of discounting effects are analyzed and shown to enjoy a straightforward explanation within the suggested theory. We also introduce a gen- eral methodology based on self-similar approximation theory for deriving the evolution equations for the probabilities of future prospects. This provides a novel classification of possible discount factors, which include the previously known cases (exponential or hyperbolic discounting), but also predicts a novel class of discount factors that decay to a strictly positive constant for very large future time horizons. This class may be useful to deal with very long-term discounting situations associated with intergenerational public policy choices, encompassing issues such as global warming and nuclear waste disposal. PACS : 89.65.-3 Social and economic systems - 89.70.Hj Communication complexity - 89.75.-k Complex systems - 03.67.Hk Quantum communication a e-mail: firstname.lastname@example.org b e-mail: email@example.com 1 1 Introduction The concept of risk is widely used in economics, finance, psychology, as well as in everyday life. Respectively, there exist several definitions of risk and different ways of evaluating it. In any application, the notion of risk is always related to the necessity of taking decisions under uncertainty. It is impossible to achieve optimal results in any science without correct decisions, leading to optimal consequences following from the taken decision. This is why the notion of risk and the problem of its evaluation has, first of all, to be understood in the frame of decision theory. It is precisely the aim of the present paper to formulate a novel approach for taking into account the risk in decision making and to demonstrate in concrete examples, related to temporal effects in making decisions, that this new approach is free of defects and paradoxes plaguing the application of standard decision theory....
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