Related papers: A quantum statistical approach to simplified stock…
We propose and discuss some toy models of stock markets using the same operatorial approach adopted in quantum mechanics. Our models are suggested by the discrete nature of the number of shares and of the cash which are exchanged in a real…
In this paper we continue our systematic analysis of the operatorial approach previously proposed in an economical context and we discuss a {\em mixed} toy model of a simplified stock market, i.e. a model in which the price of the shares is…
In this paper we continue our descriptions of stock markets in terms of some non abelian operators which are used to describe the portfolio of the various traders and other {\em observable} quantities. After a first prototype model with…
A new model for stocks markets using integer values for each stock price is presented. In contrast with previously reported models, the variables used in the model are not of binary type, but of more general integer type. It is shown how…
This brief article gives an overview of quantum mechanics as a {\em quantum probability theory}. It begins with a review of the basic operator-algebraic elements that connect probability theory with quantum probability theory. Then quantum…
Quantum theory is used to model secondary financial markets. Contrary to stochastic descriptions, the formalism emphasizes the importance of trading in determining the value of a security. All possible realizations of investors holding…
New theoretical approaches about forecasting stock markets are proposed. A mathematization of the stock market in terms of arithmetical relations is given, where some simple (non-differential, non-fractal) expressions are also suggested as…
A statistical physics model for the time evolutions of stock portfolios is proposed. In this model the time series of price changes are coded into the sequences of up and down spins. The Hamiltonian of the system is introduced and is…
Beginning with several basic hypotheses of quantum mechanics, we give a new quantum model in econophysics. In this model, we define wave functions and operators of the stock market to establish the Schr\"odinger equation for the stock…
We generalize classical statistical mechanics to describe the kinematics and the dynamics of systems whose variables are constrained by a single quantum postulate (discreteness of the spectrum of values of at least one variable of the…
It is believed by the majority today that the efficient market hypothesis is imperfect because of market irrationality. Using the physical concepts and mathematical structures of quantum mechanics, we construct an econophysics framework for…
Modern approaches to stock pricing in quantitative finance are typically founded on the 'Black-Scholes model' and the underlying 'random walk hypothesis'. Empirical data indicate that this hypothesis works well in stable situations but, in…
This paper initiates a study into the century-old issue of market predictability from the perspective of computational complexity. We develop a simple agent-based model for a stock market where the agents are traders equipped with simple…
A full treatment for the scattering of an arbitrary number of bosons through a Bell multiport beam splitter is presented that includes all possible output arrangements. Due to exchange symmetry, the event statistics differs dramatically…
A surprising image of the stock market arises if the price time series of all Dow Jones Industrial Average stock components are represented in one chart at once. The chart evolves into a braid representation of the stock market by taking…
We generalize the recently proposed quantum model for the stock market by Zhang and Huang to make it consistent with the discrete nature of the stock price. In this formalism, the price of the stock and its trend satisfy the generalized…
Identical quantum particles exhibit only two types of statistics: bosonic and fermionic. Theoretically, this restriction is commonly established through the symmetrization postulate or (anti)commutation constraints imposed on the algebra of…
The outcome statistics of an informationally complete quantum measurement for a system in a given state can be used to evaluate the ensemble expectation of any linear operator in the same state, by averaging a function of the outcomes that…
We generalize Taylor's theorem by introducing a stochastic formulation based on an underlying Poisson point process model. We utilize this approach to propose a novel non-linear regression framework and perform statistical inference of the…
The present paper describes a practical example in which the probability distribution of the prices of a stock market blue chip is calculated as the wave function of a quantum particle confined in a potential well. This model may naturally…