Quantum Bohmian-Inspired Potential to Model Non-Gaussian Time Series and Its Application in Financial Markets.

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.

Causal viewpoint and ensemble interpretation: from physics to the social sciences.

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)'.

Thermodynamics 2.0: Bridging the natural and social sciences.

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)'.

Using the Quantum Potential in Elementary Portfolio Management: Some Initial Ideas.

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.

Process mining with real world financial loan applications: Improving inference on incomplete event logs.

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.

Quantum generalized observables framework for psychological data: a case of preference reversals in US elections.

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. ScriptaT163, 014010 (doi:10.1088/0031-8949/2014/T163/014010); Khrennikova & Haven 2016 Phil. Trans. R. Soc. A374, 20150106 (doi:10.1098/rsta.2015.0106); Smith et al. 1999 Am. J. Polit. Sci.43, 737-764 (doi:10.2307/2991833)). 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. A374, 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 non-double 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'.

Links between fluid mechanics and quantum mechanics: a model for information in economics?

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.

Instability of political preferences and the role of mass media: a dynamical representation in a quantum framework.

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.

Two types of potential functions and their use in the modeling of information: two applications from the social sciences.

In this paper we consider how two types of potential functions, the real and quantum potential can be shown to be of use in a social science context. The real potential function is a key ingredient in the Hamiltonian framework used in both classical and quantum mechanics. The quantum potential however emerges in a different way in quantum mechanics. In this paper we consider both potentials and we attempt to give them a social science interpretation within the setting of two applications.

The role of recurrence plots in characterizing the output-unemployment relationship: an analysis.

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.