Related papers: A quantum model for the stock market
Adaptive wave model for financial option pricing is proposed, as a high-complexity alternative to the standard Black--Scholes model. The new option-pricing model, representing a controlled Brownian motion, includes two wave-type approaches:…
In recent years there has been a closer interrelationship between several scientific areas trying to obtain a more realistic and rich explanation of the natural and social phenomena. Among these it should be emphasized the increasing…
We derive the classical equations of hydrodynamic type (Euler equation and the continuity equation) from which the Schrodinger equation follows as a limit case. It is shown that the statistical ensemble corresponding to quantum system and…
Pricing financial derivatives, in particular European-style options at different time-maturities and strikes, means a relevant problem in finance. The dynamics describing the price of vanilla options when constant volatilities and interest…
The importance of considering the volumes to analyze stock prices movements can be considered as a well-accepted practice in the financial area. However, when we look at the scientific production in this field, we still cannot find a…
The solution of option-pricing problems may turn out to be computationally demanding due to non-linear and path-dependent payoffs, the high dimensionality arising from multiple underlying assets, and sophisticated models of price dynamics.…
A semiclassical Quantum Hydrodynamic model has been derived by taking the moments of the Wigner-Boltzmann equation. For the first time, the closure has been achieved by the use of the momentum shifted version of all order quantum corrected…
We investigate the quantum cosmological tunneling scenario for inflationary models. Within a path-integral approach, we derive the corresponding tunneling probability distribution. A sharp peak in this distribution can be interpreted as the…
We study the optimal investment problem for a continuous time incomplete market model such that the risk-free rate, the appreciation rates and the volatility of the stocks are all random; they are assumed to be independent from the driving…
In this paper we provide a comprehensive analysis of a structural model for the dynamics of prices of assets traded in a market originally proposed in [1]. The model takes the form of an interacting generalization of the geometric Brownian…
Accurate modeling of the temporal evolution of asset prices is crucial for understanding financial markets. We explore the potential of discrete-time quantum walks to model the evolution of asset prices. Return distributions obtained from a…
We study a financial model with a non-trivial price impact effect. In this model we consider the interaction of a large investor trading in an illiquid security, and a market maker who is quoting prices for this security. We assume that the…
From its beginning, there have been attempts by physicists to formulate quantum mechanics without requiring the use of wave functions. An interesting recent approach takes the point of view that quantum effects arise solely from the…
This paper considers the extension of the non-Markovian stochastic approach for quantum open systems strongly coupled to a fermionic bath, to the models in which the system operators commute with the fermion bath. This technique can also be…
This paper describes an approach to economics that is inspired by quantum computing, and is motivated by the need to develop a consistent quantum mathematical framework for economics. The traditional neoclassical approach assumes that…
Using a simple geometrical construction based upon the linear action of the Heisenberg--Weyl group we deduce a new nonlinear Schr\"{o}dinger equation that provides an exact dynamic and energetic model of any classical system whatsoever, be…
The purpose of the paper is to study the foundations of the main axioms of Quantum Mechanics. From a general study of the mathematical properties of the models used in Physics to represent systems, we prove that the states of a system can…
A new energy-based stochastic extension of the Schrodinger equation for which the wave function collapses after the passage of a finite amount of time is proposed. An exact closed-form solution to the dynamical equation, valid for all…
The quantum dynamic equation (QDE) of machine learning is obtained based on Schr\"odinger equation and potential energy equivalence relationship. Through Wick rotation, the relationship between quantum dynamics and thermodynamics is also…
Model uncertainty is a type of inevitable financial risk. Mistakes on the choice of pricing model may cause great financial losses. In this paper we investigate financial markets with mean-volatility uncertainty. Models for stock markets…