Related papers: Quantum diffusion of prices and profits
In this paper we reformulate the problem of pricing options in a quantum setting. Our proposed algorithm involves preparing an initial state, representing the option price, and then evolving it using existing imaginary time simulation…
With the goal in mind of deriving a method to compute quantum corrections for the real-time evolution in quantum field theory, we analyze the problem from the perspective of the Wigner function. We argue that this provides the most natural…
Quantum-classical molecular dynamics, as a partial classical limit of the full quantum Schr\"odinger equation, is a widely used framework for quantum molecular dynamics. The underlying equations are nonlinear in nature, containing a quantum…
We analyze the problem of the analytical characterization of the probability distribution of financial returns in the exponential Ornstein-Uhlenbeck model with stochastic volatility. In this model the prices are driven by a Geometric…
Most energy and commodity markets exhibit mean-reversion and occasional distinctive price spikes, which results in demand for derivative products which protect the holder against high prices. To this end, in this paper we present exact and…
We introduce and discuss a nonlinear kinetic equation of Boltzmann type which describes the influence of knowledge in the evolution of wealth in a system of agents which interact through the binary trades introduced in Cordier, Pareschi,…
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…
We introduce a multivariate Hawkes process that accounts for the dynamics of market prices through the impact of market order arrivals at microstructural level. Our model is a point process mainly characterized by 4 kernels associated with…
In the recent years, mater-wave interferometry has attracted growing attention due to its unique suitability for high-precision measurements and study of fundamental aspects of quantum theory. Diffraction and interference of matter waves…
We analyze in detail the discrete--time quantum walk on the line by separating the quantum evolution equation into Markovian and interference terms. As a result of this separation, it is possible to show analytically that the quadratic…
We study the quantum evolution under the combined action of the exponentials of two not necessarily commuting operators. We consider the limit in which the two evolutions alternate at infinite frequency. This case appears in a plethora of…
The quest of this work is to present discussions of some fundamental questions of economics in the era of quantum technology, which require a treatment different from economics studied thus far in the literature. A study of quantum economic…
The Quantum Decision Theory, developed recently by the authors, is applied to clarify the role of risk and uncertainty in decision making and in particular in relation to the phenomenon of dynamic inconsistency. By formulating this notion…
In the paper, we discuss the studies of mathematical models of diffusion scattering of waves in the phase space, and relation of these models with quantum mechanics. In the previous works it is shown that in these models of classical…
The analysis of diffusive energy spreading in quantized chaotic driven systems, leads to a universal paradigm for the emergence of a quantum anomaly. In the classical approximation a driven chaotic system exhibits stochastic-like diffusion…
We derive an analytical expression of a Wigner function that approximately describes the time evolution of the one-dimensional motion of a particle in a nonharmonic potential. Our method involves two exact frame transformations, accounting…
Time flow has been embodied in time-dependent Schroedinger equation representing one of the foundations of quantum mechanics. Pauli's criticism (1933) has, however, indicated that the assumptions concerning representation Hilbert space have…
We consider the pricing problem related to payoffs that can have discontinuities of polynomial growth. The asset price dynamic is modeled within the Black and Scholes framework characterized by a stochastic volatility term driven by a…
In this paper we introduce kinetic equations for the evolution of the probability distribution of two goods among a huge population of agents. The leading idea is to describe the trading of these goods by means of some fundamental rules in…
We establish the correspondence between the classical and quantum butterfly effects in nonlinear vector mechanics with the broken $O(N)$ symmetry. On one hand, we analytically calculate the out-of-time ordered correlation functions and the…