arXiv research

We introduce a novel description of the dynamics of the order book of financial markets as that of an effective colloidal Brownian particle embedded in fluid particles. The analysis of a comprehensive market data enables us to identify all motions of the fluid particles. Correlations between the motions of the Brownian…

We study systems of Brownian particles on the real line, which interact by splitting the local times of collisions among themselves in an asymmetric manner. We prove the strong existence and uniqueness of such processes and identify them with the collections of ordered processes in a Brownian particle system, in which …

Mean exit times concentrate near equators and minimal hypersurfaces in high dimensions.

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 explain the operation of several empirical rules used by technical analysts. Mod…

We pursue the quantum-mechanical challenge to the efficient market hypothesis for the stock market by employing the quantum Brownian motion model. We utilize the quantum Caldeira-Leggett master equation as a possible phenomenological model for the stock-market-prices fluctuations while introducing the external harmonic…

Model tracks structural changes in Brownian particle configurations on a sphere.

Paper tackles rough volatility estimation from high-frequency data.

We generalise the description of the dynamics of the order book of financial markets in terms of a Brownian particle embedded in a fluid of incoming, exiting and annihilating particles by presenting a model of the velocity on each side (buy and sell) independently. The improved model builds on the time-averaged number …

Machine learning predicts phase behavior in active matter suspensions.

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 the stock market, based on which we analogously map massive numbers of single s…

Neural network models colloidal particle dynamics in non-equilibrium systems.

We propose a simple model for the behaviour of longterm investors on a stock market, consisting of three particles, which represent the current price of the stock and the opinion of the buyers, respectively sellers, about the right trading price. As time evolves, both groups of traders update their opinions with respec…

GER learns particle dynamics from unpaired snapshots using physics-informed GANs.

The model describing market dynamics after a large financial crash is considered in terms of the stochastic differential equation of Ito. Physically, the model presents an overdamped Brownian particle moving in the nonstationary one-dimensional potential $U$ under the influence of the variable noise intensity, dependin…

In this paper a simple model for the evolution of the forward density of the future value of an asset is proposed. The model allows for a straightforward initial calibration to option prices and has dynamics that are consistent with empirical findings from option price data. The model is constructed with the aim of bei…

Accelerates sampling from Gibbs distributions using ARWP method.

Quasi-equilibrium models for aggregate variables are widely-used throughout finance and economics. The validity of such models depends crucially upon assuming that the systems' participants behave both independently and in a Markovian fashion. We present a simplified market model to demonstrate that herding effects bet…

In classical optimal transport, the contributions of Benamou-Brenier and McCann regarding the time-dependent version of the problem are cornerstones of the field and form the basis for a variety of applications in other mathematical areas. We suggest a Benamou-Brenier type formulation of the martingale transport proble…

We study the mean escape time in a market model with stochastic volatility. The process followed by the volatility is the Cox Ingersoll and Ross process which is widely used to model stock price fluctuations. The market model can be considered as a generalization of the Heston model, where the geometric Brownian motion…

Study on ion travel time on curved surfaces.

Unified framework for Brownian motion distances on specific geometric manifolds.

Continuous time random walks impose a random waiting time before each particle jump. Scaling limits of heavy tailed continuous time random walks are governed by fractional evolution equations. Space-fractional derivatives describe heavy tailed jumps, and the time-fractional version codes heavy tailed waiting times. Thi…

Continuous time random walks (CTRWs) are used in physics to model anomalous diffusion, by incorporating a random waiting time between particle jumps. In finance, the particle jumps are log-returns and the waiting times measure delay between transactions. These two random variables (log-return and waiting time) are typi…

We obtain upper bounds for the isoperimetric quotients of extrinsic balls of submanifolds in ambient spaces which have a lower bound on their radial sectional curvatures. The submanifolds are themselves only assumed to have lower bounds on the radial part of the mean curvature vector field and on the radial part of the…

Develops a neural network approach to solve inverse stochastic problems from particle observations.

Enhanced feature learning using neural networks and kernel methods with improved robustness.

We extend a model of positive feedback and contagion in large mean-field systems, by introducing a common source of noise driven by Brownian motion. Although the driving dynamics are continuous, the positive feedback effect can lead to `blow-up' phenomena whereby solutions develop jump-discontinuities. Our main results…

With $(X,\mathfrak{d},\mathfrak{m})$ an $\mathrm{RCD}^*(K,N)$ space for some $K\in\mathbf{R}$, $N\in [1,\infty)$, let $H$ be the self-adjoint Laplacian induced by the underlying Cheeger form. Given $α\in [0,1]$ we introduce the $α$-Kato class of potentials on $(X,\mathfrak{d},\mathfrak{m})$, and given a potential $V:X\…

New insights show stochastic initialization prevents token clustering in deep Transformers.

By Gyongy's theorem, a local and stochastic volatility (LSV) model is calibrated to the market prices of all European call options with positive maturities and strikes if its local volatility function is equal to the ratio of the Dupire local volatility function over the root conditional mean square of the stochastic v…

Researchers created a continuous Markov martingale that mimics Brownian motion but lacks the strong Markov property.

Study on determinants of unitary Brownian motion and their asymptotic laws.

A nonlinear wave alternative for the standard Black-Scholes option-pricing model is presented. The adaptive-wave model, representing 'controlled Brownian behavior' of financial markets, is formally defined by adaptive nonlinear Schrödinger (NLS) equations, defining the option-pricing wave function in terms of the stock…

Study refracted skew Brownian motion, find densities and asymptotics.

New model uses generalized fractional Brownian motion for stock price prediction.

Study Brownian loops on hyperbolic surfaces, linking to Selberg zeta function.

Paper defines multi-dimensional fractional Brownian motion under volatility uncertainty.

Researchers calculate the Laplace transform of a geometric Brownian motion integral.

A computer vision approach improves neutral particle detection in particle flow algorithms.

Jointly estimates flow fields and particle properties from Lagrangian data.

Proves CLT for Brownian paths on pinched negative curvature manifolds.

Geodesic walks converge to Brownian motion on Finsler manifolds.

Estimates log-likelihood of interacting particle systems using virtual particles.

Universal approximation for stochastic processes using Brownian motion.

New SDEs use $G$-Brownian motion, extending mean-field models.

This paper optimizes functions of probability measures using particle gradient descent for displacement convex functions.

A new model captures option price dynamics using sub-fractional Brownian motion.

The paper connects Riemann surface length spectra to Brownian loop measures.