Related papers: Modelling Illiquid Stocks Using Quantum Stochastic…
The Fokker--Planck equation is a key ingredient of many models in physics, and related subjects, and arises in a diverse array of settings. Analytical solutions are limited to special cases, and resorting to numerical simulation is often…
Quantum Portfolios of quantum algorithms encoded on qbits have recently been reported. In this paper a discussion of the continuous variables version of quantum portfolios is presented. A risk neutral valuation model for options dependent…
We describe quantum-field-theoretical (QFT) techniques for mapping quantum problems onto c-number stochastic problems. This approach yields results which are identical to phase-space techniques [C.W. Gardiner, {\em Quantum Noise} (1991)]…
Cosmic inflation may exhibit stochastic periods during which quantum fluctuations dominate over the semi-classical evolution. Extracting observables in these regimes is a notoriously difficult program as quantum randomness makes them fully…
We study the nonstationary solutions of Fokker-Planck equations associated to either stationary or nonstationary quantum states. In particular we discuss the stationary states of quantum systems with singular velocity fields. We introduce a…
We investigate a stochastic approach to non-equilibrium quantum spin systems based on recent insights linking quantum and classical dynamics. Exploiting a sequence of exact transformations, quantum expectation values can be recast as…
An implicit and conservative numerical scheme is proposed for the isotropic quantum Fokker-Planck equation describing the evolution of degenerate electrons subject to elastic collisions with other electrons and ions. The electron-ion and…
The Accardi-Boukas quantum Black-Scholes equation can be used as an alternative to the classical approach to finance, and has been found to have a number of useful benefits. The quantum Kolmogorov backward equations, and associated quantum…
We model thermostatic devices using a stochastic hybrid description, and introduce an external actuation mechanism that creates random switch events in the discrete dynamics. We then conjecture the form of the Fokker-Planck equation and…
We propose a model based on coupled multiplicative stochastic processes to understand the dynamics of competing species in an ecosystem. This process can be conveniently described by a Fokker-Planck equation. We provide an analytical…
Stochastic processes play a fundamental role in physics, mathematics, engineering and finance. One potential application of quantum computation is to better approximate properties of stochastic processes. For example, quantum algorithms for…
The problem of portfolio optimization when stochastic factors drive returns and volatilities has been studied in previous works by the authors. In particular, they proposed asymptotic approximations for value functions and optimal…
Inspired by the modeling of grain growth in polycrystalline materials, we consider a nonlinear Fokker-Plank model, with inhomogeneous diffusion and with variable mobility parameters. We develop large time asymptotic analysis of such…
A stochastic treatment yielding to the derivation of a general Fokker-Planck equation is presented to model the slow convergence towards equilibrium of mean-field systems due to finite-N effects. The thermalization process involves notably…
Following on from our recent work, we investigate a stochastic approach to non-equilibrium quantum spin systems. We show how the method can be applied to a variety of physical observables and for different initial conditions. We provide…
In this paper we focus on the construction of numerical schemes for nonlinear Fokker-Planck equations that preserve the structural properties, like non negativity of the solution, entropy dissipation and large time behavior. The methods…
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 article present a continuous cascade model of volatility formulated as a stochastic differential equation. Two independent Brownian motions are introduced as random sources triggering the volatility cascade. One multiplicatively…
The continuous time stochastic process is a mainstream mathematical instrument modeling the random world with a wide range of applications involving finance, statistics, physics, and time series analysis, while the simulation and analysis…
The Fokker-Planck equations for stochastic dynamical systems, with non-Gaussian $\alpha-$stable symmetric L\'evy motions, have a nonlocal or fractional Laplacian term. This nonlocality is the manifestation of the effect of non-Gaussian…