A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
We analyze the impact of the sampling interval on the estimation of Kramers-Moyal coefficients. We obtain the finite-time expressions of these coefficients for several standard processes. We also analyze extreme situations such as the independence and no-fluctuation limits that constitute useful references. Our results…
Study examines USD exchange rate dynamics using Kramers-Moyal expansion.
This research develops an evolutionary approach to discover non-Gaussian stochastic dynamical systems.
New method handles complex systems with discontinuous, heavy-tailed noise.
New method extracts stochastic laws from data, including Lévy noise.
Unified framework maps financial market dynamics using TE and KM, revealing directional information flow.
Study shows different price correlations in European electricity markets.
Method extracts stochastic systems with Lévy noise from data.
Method extracts governing laws from non-Gaussian stochastic systems data.
We study the evolution of probability distribution functions of returns, from the tick data of the Korean treasury bond (KTB) futures and the S$&$P 500 stock index, which can be described by means of the Fokker-Planck equation. We show that the Fokker-Planck equation and the Langevin equation from the estimated Kramers…
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 under the influence of the variable noise intensity, dependin…
The Accardi-Boukas quantum Black-Scholes framework, provides a means by which one can apply the Hudson-Parthasarathy quantum stochastic calculus to problems in finance. Solutions to these equations can be modelled using nonlocal diffusion processes, via a Kramers-Moyal expansion, and this provides useful tools to under…
We solve the dynamics of the on-line minority game, with general types of decision noise, using generating functional techniques a la De Dominicis and the temporal regularization procedure of Bedeaux et al. The result is a macroscopic dynamical theory in the form of closed equations for correlation- and response functi…
In complex systems such as turbulent flows and financial markets, the dynamics in long and short time-lags, signaled by Gaussian and fat-tailed statistics, respectively, calls for a unified description. To address this issue we analyze a real dataset, namely, price fluctuations, in a wide range of temporal scales to em…
Novel framework discovers SPDEs from limited data.
The evolution of the probability distributions of Japan and US major market indices, NIKKEI 225 and NASDAQ composite index, and and currency exchange rates is described by means of the Fokker-Planck equation (FPE). In order to distinguish and quantify the deterministic and random influences on these…
The most common stochastic volatility models such as the Ornstein-Uhlenbeck (OU), the Heston, the exponential OU (ExpOU) and Hull-White models define volatility as a Markovian process. In this work we check of the applicability of the Markovian approximation at separate times scales and will try to answer the question …
Our purpose is to relate the Fokker-Planck formalism proposed by [Friedrich et al., Phys. Rev. Lett. 84, 5224 (2000)] for the distribution of stock market returns to the empirically well-established power law distribution with an exponent in the range 3-5. We show how to use Friedrich et al.'s formalism to predict that…
This work extracts stochastic dynamical systems with -stable Lévy noise.
Proposes a probabilistic digital twin for dynamical systems using sparse Bayesian learning.