Related papers: Finite quantum mechanical model for the stock mark…
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…
Diffusion processes driven by Fractional Brownian motion (FBM) have often been considered in modeling stock price dynamics in order to capture the long range dependence of stock price observed in reality. Option prices for such models had…
A deterministic model with a large number of continuous and discrete degrees of freedom is described, and a statistical treatment is proposed. The model exactly obeys a Schrodinger equation, which has to be interpreted exactly according to…
Quantum computers have the potential to provide an advantage for financial pricing problems by the use of quantum estimation. In a broader context, it is reasonable to ask about situations where the market and the assets traded on the…
The paper treats the financial market as a communication system, using four information-theoretic assumptions to derive an idealized model with only one parameter. State variables are scalar stationary diffusions. The model minimizes the…
Applications of Quantum Tunneling effect have long gone beyond the traditional physical meaning. Initially created by Gamow to explain {\alpha}-decay of nuclear particles, along the time, quantum tunneling found fertile domain of research…
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…
The present authors have put forward a quantum game theory based model of market prices movements. By using Fisher information, we present a construction of an equation of Schr\"{o}dinger type for probability distributions for relationship…
I propose a version of quantum mechanics featuring a discrete and finite number of states that is plausibly a model of the real world. The model is based on standard unitary quantum theory of a closed system with a finite-dimensional…
A derivative is a financial security whose value is a function of underlying traded assets and market outcomes. Pricing a financial derivative involves setting up a market model, finding a martingale (``fair game") probability measure for…
We investigate the behavior of stocks in daily price-limited stock markets by purposing a quantum spatial-periodic harmonic model. The stock price is presumed to oscillate and damp in a quantum spatial-periodic harmonic oscillator potential…
Universality of quantum mechanics -- its applicability to physical systems of quite different nature and scales -- indicates that quantum behavior can be a manifestation of general mathematical properties of systems containing…
We start with a discussion of the use of mathematics to model the real world then justify the role of Hilbert space formalism for such modelling in the general context of quantum logic. Following this, the incompleteness of the…
An explicit formula is derived for the value of weak information in a discrete time model that works for a wide range of utility functions including the logarithmic and power utility. We assume a complete market with a finite number of…
Quantum game theory, whatever opinions may be held due to its abstract physical formalism, have already found various applications even outside the orthodox physics domain. In this paper we introduce the concept of a quantum auction, its…
This paper summarizes a research program that has been underway for a decade. The objective is to find a fast and accurate scheme for solving quantum problems which does not involve a Monte Carlo algorithm. We use an alternative strategy…
In this article we look at stochastic processes with uncertain parameters, and consider different ways in which information is obtained when carrying out observations. For example we focus on the case of a the random evolution of a traded…
We consider a rational agent who at time $0$ enters into a financial contract for which the payout is determined by a quantum measurement at some time $T>0$. The state of the quantum system is given in the Heisenberg representation by a…
An adapted representation of quantum mechanics sheds new light on the relationship between quantum states and classical states. In this approach the space of quantum states splits into a product of the state space of classical mechanics and…
We consider some basic problems associated with quantum mechanics of systems having a time-dependent Hilbert space. We provide a consistent treatment of these systems and address the possibility of describing them in terms of a…