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In this article, we assert that, for the construction of quantum physics-analogous (as opposed to quantum math-analogous) probabilistic models of the social (e.g. economics–financial) reality, the use of the notion of causality and the idea of an ensemble of similarly prepared systems in a socially analogous manner could be essential. We give plausibility arguments in favour of this assertion by considering two social situations describable in terms of discrete-time stochastic (i.e. Markov) processes. The first one is an arbitrary economics/financial context expressed as a temporal sequence of actualized social states (e.g. decisions, choices, preferences, etc.). The other one is more specific, involving a generic supply chain context. This article is part of the theme issue 'Thermodynamics 2.0: Bridging the natural and social sciences (Part 1)'. [ABSTRACT FROM AUTHOR]

In this work, we analyse and model a real life financial loan application belonging to a sample bank in the Netherlands. The event log is robust in terms of data, containing a total of 262 200 event logs, belonging to 13 087 different credit applications. The goal is to work out a decision model, which represents the underlying tasks that make up the loan application service. To this end we study the impact of incomplete event logs (for instance workers forget to register their tasks). The absence of data is translated into a drastic decrease of precision and compromises the decision models, leading to biased and unrepresentative results. We use non-classical probability to show we can better reduce the error percentage of inferences as opposed to classical probability. [ABSTRACT FROM AUTHOR]

Politics is regarded as a vital area of public choice theory, and it is strongly relying on the assumptions of voters' rationality and as such, stability of preferences. However, recent opinion polls and real election outcomes in the USA have shown that voters often engage in 'ticket splitting', by exhibiting contrasting party support in Congressional and Presidential elections (cf. Khrennikova 2014 Phys. Scripta T163, 014010 (doi:10.1088/0031-8949/2014/T163/014010); Khrennikova & Haven 2016 Phil. Trans. R. Soc. A 374, 20150106 (doi:10.1098/rsta.2015.0106); Smith et al. 1999 Am. J. Polit. Sci. 43, 737-764 (doi:10.2307/2991 833)). Such types of preference reversals cannot be mathematically captured via the formula of total probability, thus showing that voters' decision making is at variance with the classical probabilistic information processing framework. In recent work, we have shown that quantum probability describes well the violation of Bayesian rationality in statistical data of voting in US elections, through the so-called interference effects of probability amplitudes. This paper is proposing a novel generalized observables framework of voting behaviour, by using the statistical data collected and analysed in previous studies by Khrennikova (Khrennikova 2015 Lect. Notes Comput. Sci. 8951, 196-209) and Khrennikova & Haven (Khrennikova & Haven 2016 Phil. Trans. R. Soc. A 374, 20150106 (doi:10.1098/rsta.2015.0106)). This framework aims to overcome the main problems associated with the quantum probabilistic representation of psychological data, namely the nondouble stochasticity of transition probability matrices. We develop a simplified construction of generalized positive operator valued measures by formulating special non-orthonormal bases with respect to these operators. This article is part of the themed issue 'Second quantum revolution: foundational questions'. [ABSTRACT FROM AUTHOR]

This paper tallies the links between fluid mechanics and quantum mechanics, and attempts to show whether those links can aid in beginning to build a formal template which is usable in economics models where time is (a)symmetric and memory is absent or present. An objective of this paper is to contemplate whether those formalisms can allow us to model information in economics in a novel way. [ABSTRACT FROM AUTHOR]

The formulation of quantum mechanics as a diffusion process by Nelson (Phys Rev 150:1079-1085, ) provides for an interesting approach on how we may transit from classical mechanics into quantum mechanics. Besides the presence of the real potential function, another type of potential function (often denoted as 'quantum potential') forms an intrinsic part of this theory. In this paper we attempt to show how both types of potential functions can have a use in a resolutely macroscopic context like financial asset pricing. We are particularly interested in uncovering how the 'quantum potential' can add to the economics-based relevant information which is already supplied by the real potential function. [ABSTRACT FROM AUTHOR]

The multifractal spectrum of a time series can be ascertained with a number of techniques, some based on wavelets, others based on the much newer (multifractal) detrended fluctuation analysis (MF-DFA). We test for the presence of multifractality in daily data on selected exchange rates from Central and Eastern European economies against EURO. The approach is based on a slight modification of the MF-DFA analysis in that local trends are not allowed to be polynomially fitted but rather are estimated through a sifting process which is established through a so called Empirical Mode Decomposition (EMD) algorithm. We assess the drivers of the multifractal spectrum strength, like temporal correlations or distributions based on surrogate data. Another topic discussed is whether the entrance in the exchange rate mechanism ERM II influenced the multifractality of the exchange rates. [ABSTRACT FROM AUTHOR]

The Gorini-Kossakowski-Sudarshan-Lindblad equation allows us to model the process of decision making in US elections. The crucial point we attempt to make is that the voter's mental state can be represented as a superposition of two possible choices for either republicans or democrats. However, reality dictates a more complicated situation: typically a voter participates in two elections, i.e. the congress and the presidential elections. In both elections the voter has to decide between two choices. This very feature of the US election system requires that the mental state is represented by a 2-qubit state corresponding to the superposition of 4 different choices. The main issue is to describe the dynamics of the voters' mental states taking into account the mental and political environment. What is novel in this paper is that we apply the theory of open quantum systems to social science. The quantum master equation describes the resolution of uncertainty (represented in the form of superposition) to a definite choice. [ABSTRACT FROM AUTHOR]

We apply methods of wave mechanics to financial modelling. We proceed by assigning a financial interpretation to wave numbers. This paper makes a plea for the use of the concept of ‘tunnelling’ (in the mathematical formalism of quantum mechanics) in the modelling of financial arbitrage. Financial arbitrage is a delicate concept to model in social science (i.e. in this case economics and finance) as its presence affects the precision of benchmark financial asset prices. In this paper, we attempt to show how ‘tunnelling’ can be used to positive effect in the modelling of arbitrage in a financial asset pricing context. [ABSTRACT FROM AUTHOR]

We analyse the output-unemployment relationship using an approach based on cross-recurrence plots and quantitative recurrence analysis. We use post-war period quarterly U.S. data. The results obtained show the emergence of a complex and interesting relationship. [ABSTRACT FROM AUTHOR]

q-derivatives are part of so called quantum calculus. In this paper we investigate how such derivatives can possibly be used in Itô's lemma. This leads us to consider how such derivatives can be used in a social science setting. We conclude that in a Itô Lemma setting we cannot use a macroscopic version of the Heisenberg uncertainty principle with q-derivatives. [ABSTRACT FROM AUTHOR]

This survey paper provides first for an overview of how quantum-like concepts could be used in macroscopic environments like economics. The paper then argues for the use of the concept of a quantum mechanical wave function as an ‘information wave function’. A rationale is provided on why such interpretation is reasonable. After having defined the ‘information wave function’, Ψ( q), we argue how | Ψ( q) |2 can be interpreted as a Radon-Nikodym derivative. We consider how we can connect, using the | Ψ( q) |2, the Blackwell and Dubins (Ann. Math. Stat. 33:882–886, ) Theorem with Rényi’s (Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, ) measure of quantity of information. We also define ‘ambiguity of information’ and ‘multi-sourced information’. [ABSTRACT FROM AUTHOR]

We define an ‘information wave function’, Ψ( q). We underline the role of risk-neutral probabilities in financial non-arbitrage. We argue how a change in the probabilities based on Ψ( q) can induce arbitrage. [ABSTRACT FROM AUTHOR]

Abstract: Analytical solutions to the backward Kolmogorov PDE are very dependent on the functional form of and . We suggest one solution technique for obtaining analytical solutions via the use of an adiabatic approximation to the Schrödinger PDE. This approximation takes the specific form of a so-called WKB (W =Wentzel [G. Wentzel, Eine Verallgemeinerung der Quantenbedingungen für die Zwecke der Wellenmechanik, Z. Phys. 38 (1926) 518–529], K =Kramers [H. Kramers, Wellenmechanik und halbzahlige Quantisierung, Z. Phys. 39 (1926) 828–840], B =Brillouin [L. Brillouin, La mécanique ondulatoire de Schrödinger: une méthode générale de résolution par approximations successives, C. R. Acad. Sci. 183 (1926) 24–26]) approximation. We provide for two examples, in financial option pricing, where we show how the proposed approximation could be of use. [Copyright &y& Elsevier]

This paper tries to argue why pilot-wave theory could be of use in financial economics. We introduce the notion of information wave. We consider a stochastic guidance equation and part of the drift term of that equation makes reference to the phase of the wave. In order to embed information in financial option pricing we could use such a drift. We also briefly argue how we could embed information in the pricing kernel of the option price. [ABSTRACT FROM AUTHOR]

Abstract: We show that if a portfolio of a financial derivative asset and a stock is put in an environment where the value of an asset (besides its price) is formalized as a superposition of price states, such portfolio may not be risk free and fuzzy preferences for risk premia may exist. We argue for a modification of the classical Brownian motion process as used in option pricing. This modification on the classical Brownian motion, we call the -Brownian motion and one specific format of this -Brownian motion can be shown to have a connection with the quantum physical Schrödinger equation. [Copyright &y& Elsevier]

Abstract: This paper considers three applications. In the first application, we use the notion of fuzzy first-order stochastic dominance as defined by De Schuymer et al. (Cycle-transitive comparison of independent random variables, J. Multivariate Anal., in press) to explain various relationships between financial arbitrage and fuzzy first-order stochastic dominance. In the second application, we contrast dominance versus stochastic dominance and we define fuzzy dominance. In the third application, we argue that there exists moderate stochastic transitivity when the cumulative distribution functions are normal and there is financial quasi-arbitrage. [Copyright &y& Elsevier]

Abstract: We introduce a particular type of Brownian motion, i.e., a Brownian motion with a diffusion coefficient containing . We show that under classical Black–Scholes methodology we can obtain a PDE with a stochastic rate of return. In this environment of `non-classical'' uncertainty valued preferences for risk may exist. [Copyright &y& Elsevier]

Abstract: We propose an interpretation of the wave-equivalent of the Black–Scholes option price. We consider Nelson''s version of the Brownian motion (Dynamical Theories of Brownian Motion, Princeton University Press, Princeton, NJ, 1967) and we use this specific motion as an input to produce a Black–Scholes PDE with a risk premium. [Copyright &y& Elsevier]

The celebrated Black-Scholes differential equation provides for the price of a financial derivative. The uncertainty environment of such option price can be described by the classical ‘bit’: a system with two possible states. This paper argues for the introduction of a different uncertainty environment characterized by the so called ‘qubit’. We obtain an information-based option price and discuss the differences between this option price and the classical option price. [Copyright &y& Elsevier]

In this paper we consider the implications of embedding the Black–Scholes option pricing model within a quantum physical setting. The option price is considered to be a state function and a potential function is found which allows the option price to satisfy the Schro¨dinger differential equation. Once this arbitrage-free potential function is obtained, we argue for the construction of a so-called ‘arbitrage’ potential function. This functional is instrumental in determining the existence of a ‘financial’ state function. We show the existence of an arbitrage-free price when the potential function converges to one. The existence of arbitrage hinges on the non-zero value of the Planck constant. This constant is then linked to a parameter which regulates the probability of occurence of strategy paths. We call this parameter the ‘belief’ parameter. We argue that it is the belief parameter which may indeed proxy arbitrage. The outcome of this paper shows that the Black–Scholes model can be captured within a quantum physical setting and that the advantages of doing so may indeed provide for a first step to include arbitrage in a natural way in an otherwise arbitrage free model. [Copyright &y& Elsevier]

Owing to the globalization of the economy, the concept of entangled markets started to form, and this occurrence has smoothed the entrance of quantum mechanics into behavioral finance. In this manuscript, we introduce quantum risk and perform an analysis on portfolio optimization by controlling the quantum potential. We apply this method to eight major indices and construct a portfolio with a minimum quantum risk. The results show quantum risk has a power law behavior with a time-scale just as a standard deviation with different exponents. [ABSTRACT FROM AUTHOR]

We search to devise a new paradigm borrowed from concepts and mathematical tools of quantum physics, to model the decision-making process of the US electorate. The statistical data of the election outcomes in the period between 2008 and 2014 is analysed, in order to explore in more depth the emergence of the so-called divided government. There is an increasing urge in the political literature which indicates that preference reversal (strictly speaking the violation of the transitivity axiom) is a consequence of the so-called non-separability phenomenon (i.e. a strong interrelation of choices). In the political science literature, non-separable behaviour is characterized by a conditioning of decisions on the outcomes of some issues of interest. An additional source of preference reversal is ascribed to the time dynamics of the voters' cognitive states, in the context of new upcoming political information. As we discuss in this paper, the primary source of political information can be attributed to the mass media. In order to shed more light on the phenomenon of preference reversal among the US electorate, we accommodate the obtained statistical data in a classical probabilistic (Kolmogorovian) scheme. Based on the obtained results, we attribute the strong ties between the voters non-separable decisions that cannot be explained by conditioning with the Bayes scheme, to the quantum phenomenon of entanglement. Second, we compute the degree of interference of voters' belief states with the aid of the quantum analogue of the formula of total probability. Lastly, a model, based on the quantum master equation, to incorporate the impact of the mass media bath is proposed. [ABSTRACT FROM AUTHOR]

Thermodynamics is a universal science. The language of thermodynamics is energy and its derivatives such as entropy and power. The physical theory of thermodynamics reigns across a full spectrum of non-living objects as well as living beings. In the traditions of the past, the dichotomy between matter and life resulted in the natural sciences studying matter while the social sciences focused on living beings. As the state of human knowledge continues to evolve, anticipating the sciences of matter (natural science) and of life (social science) becoming unified under a single overarching theory is not unnatural. This article is part of the theme issue 'Thermodynamics 2.0: Bridging the natural and social sciences (Part 1)'. [ABSTRACT FROM AUTHOR]

We have implemented quantum modeling mainly based on Bohmian mechanics to study time series that contain strong coupling between their events. Compared to time series with normal densities, such time series are associated with rare events. Hence, employing Gaussian statistics drastically underestimates the occurrence of their rare events. The central objective of this study was to investigate the effects of rare events in the probability densities of time series from the point of view of quantum measurements. For this purpose, we first model the non-Gaussian behavior of time series using the multifractal random walk (MRW) approach. Then, we examine the role of the key parameter of MRW, λ , which controls the degree of non-Gaussianity, in quantum potentials derived for time series. Our Bohmian quantum analysis shows that the derived potential takes some negative values in high frequencies (its mean values), then substantially increases, and the value drops again for rare events. Thus, rare events can generate a potential barrier in the high-frequency region of the quantum potential, and the effect of such a barrier becomes prominent when the system transverses it. Finally, as an example of applying the quantum potential beyond the microscopic world, we compute quantum potentials for the S&P financial market time series to verify the presence of rare events in the non-Gaussian densities and demonstrate deviation from the Gaussian case. [ABSTRACT FROM AUTHOR]

We prove a theorem which shows that a collection of experimental data of probabilistic weights related to decisions with respect to situations and their disjunction cannot be modeled within a classical probabilistic weight structure in case the experimental data contain the effect referred to as the 'disjunction effect' in psychology. We identify different experimental situations in psychology, more specifically in concept theory and in decision theory, and in economics (namely situations where Savage's Sure-Thing Principle is violated) where the disjunction effect appears and we point out the common nature of the effect. We analyze how our theorem constitutes a no-go theorem for classical probabilistic weight structures for common experimental data when the disjunction effect is affecting the values of these data. We put forward a simple geometric criterion that reveals the non classicality of the considered probabilistic weights and we illustrate our geometrical criterion by means of experimentally measured membership weights of items with respect to pairs of concepts and their disjunctions. The violation of the classical probabilistic weight structure is very analogous to the violation of the well-known Bell inequalities studied in quantum mechanics. The no-go theorem we prove in the present article with respect to the collection of experimental data we consider has a status analogous to the well known no-go theorems for hidden variable theories in quantum mechanics with respect to experimental data obtained in quantum laboratories. Our analysis puts forward a strong argument in favor of the validity of using the quantum formalism for modeling the considered psychological experimental data as considered in this paper. [ABSTRACT FROM AUTHOR]

Price without transaction makes no sense. Trading volume authenticates its corresponding price, so there exists mutual information and correlation between price and trading volume. We are curious about fractal features of this correlation and need to know how structures in different scales translate information. To explore the influence of investment size (trading volume), price-wise (gain/loss), and time-scale effects, we analyzed the price and trading volume and their coupling by applying the MF-DXA method. Our results imply that price, trading volume and price–volume coupling exhibit a power law and are also multifractal. Meanwhile, considering developed markets, the price–volume couplings are significantly negatively correlated. However, in emerging markets, price has less of a contribution in price–volume coupling. In emerging markets in comparison with the developed markets, trading volume and price are more independent. • The results compare multifractality in the price–volume coupling for the developed and the emerging markets. • In the developed markets – on the contrary to the emerging markets – the price–volume coupling is negatively stronger. [ABSTRACT FROM AUTHOR]