Emmanuel Haven

Quantum social science

Preface Part I. Physics Concepts in Social Science? A Discussion: 1. Classical, statistical and quantum mechanics: all in one 2. Econophysics: statistical physics and social science 3. Quantum social science: a non-mathematical motivation Part II. Mathematics and Physics Preliminaries: 4. Vector calculus and other mathematical preliminaries 5. Basic elements of quantum mechanics 6. Basic elements of Bohmian mechanics Part III. Quantum Probabilistic Effects in Psychology: Basic Questions and Answers: 7. A brief overview 8. Interference effects in psychology - an introduction 9. A quantum-like model of decision making Part IV. Other Quantum Probabilistic Effects in Economics, Finance and Brain Sciences: 10. Financial/economic theory in crisis 11. Bohmian mechanics in finance and economics 12. The Bohm-Vigier Model and path simulation 13. Other applications to economic/financial theory 14. The neurophysiological sources of quantum-like processing in the brain Conclusion Glossary Index.

A discussion on embedding the Black–Scholes option pricing model in a quantum physics setting

Abstract 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 Schrodinger 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.

De-noising option prices with the wavelet method

Financial time series are known to carry noise. Hence, techniques to de-noise such data deserve great attention. Wavelet analysis is widely used in science and engineering to de-noise data. In this paper we show, through the use of Monte Carlo simulations, the power of the wavelet method in the de-noising of option price data. We also find that the estimation of risk-neutral density functions and out-of-sample price forecasting is significantly improved after noise is removed using the wavelet method.

A Black-Scholes Schrödinger option price: ‘bit’ versus ‘qubit’

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.

Bohmian Mechanics In A Macroscopic Quantum System

In the so called ‘causal’ interpretation of quantum mechanics, an electron is considered as a particle and such particle is influenced not only by a classical but also by a so called quantum potential. This idea was developed by Professor Bohm in an important paper. In this paper we use some of the basics of this interpretation in a financial option pricing environment. The causal interpretation allows for trajectories. Path breaking work by Professors Bohm and Hiley and Khrennikov and Choustova have made that the causal interpretation is a step closer to potential applications in social science. In this paper we consider the wave function as a wave of information. We consider the gradient of the phase of this wave function and show how the option price could be influenced by this gradient.

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.

Quantum Experimental Data in Psychology and Economics

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.

First results on applying a non-linear effect formalism to alliances between political parties and buy and sell dynamics

We discuss a non linear extension of a model of alliances in politics, recently proposed by one of us. The model is constructed in terms of operators, describing the interest of three parties to form, or not, some political alliance with the other parties. The time evolution of what we call the decision functions is deduced by introducing a suitable Hamiltonian, which describes the main effects of the interactions of the parties amongst themselves and with their environments, which are generated by their electors and by people who still have no clear idea for which party to vote (or even if to vote). The Hamiltonian contains some non-linear effects, which takes into account the role of a party in the decision process of the other two parties.

The role of information in a two-traders market

In a very simple stock market, made by only two initially equivalent traders, we discuss how the information can affect the performance of the traders. More in detail, we first consider how the portfolios of the traders evolve in time when the market is closed. After that, we discuss two models in which an interaction with the outer world is allowed. We show that, in this case, the two traders behave differently, depending on (i) the amount of information which they receive from outside; and (ii) the quality of this information.

Optimal Investment Strategy via Interval Arithmetic

This paper studies the optimal replacement policy of an item that experiences stochastic geometric growth in maintenance costs. The model integrates corporate taxes, tax credits, depreciation, and salvage value. We extend this traditional application to cover the cost of replacement with the payout from two bonds. The two-bond portfolio is passively immunized. The intersections between the continuation and replacement boundaries are computed using the Interval-Newton Generalized-Bisection (IN/GB) method. We allow small fluctuations of the replacement boundary. With these fluctuations, multiple intersections of the two boundaries are determined. The IN/GB method finds all these intersections without the need for initial guesses of the problem variables. This is a major computational improvement over traditional single-root finding implementations that require multiple initial guesses and provide no guarantees of existence or uniqueness. We demonstrate that without fluctuations one would expect to find a single optimal replacement time. However with fluctuations, there are several intersections of the continuation and replacement boundaries and the bond weight fractions may change by more than 200% between intersection points. These large changes in portfolio wealth allocation highlight the fragility of the idealized solution in the realm of fluctuations in replacement costs.