FMMNN combines sine activations with multi-component, multi-layer structure for high-frequency function approximation.
problem Effective representation and learning of high-frequency features in neural networks.
method Introduces FMMNN with sine-type activations and multi-component, multi-layer structure.
result FMMNN achieves strong accuracy and favorable convergence on oscillatory function-approximation benchmarks.
In this paper, we propose the idea of radial scaling in frequency domain and activation functions with compact support to produce a multi-scale DNN (MscaleDNN), which will have the multi-scale capability in approximating high frequency and high dimensional functions and speeding up the solution of high dimensional PDEs…
Stochastic methods improve data assimilation with high-frequency sensor data.
problem Computational challenges in data assimilation with high-frequency sensor data.
method Adapted stochastic approximation methods to handle high-frequency observations.
result Produces high-quality estimates using all observations without compromising statistical accuracy.
Trains a neural network to predict high-frequency trading outcomes.
problem Predicting the fill probability function for high-frequency trading.
method High-quality high-frequency data and neural network training with a weighted loss function.
result Strong state dependence properties of the fill probability function.
Two-layer networks struggle with high frequencies due to numerical and computational limitations.
problem High frequency approximation and learning in shallow networks.
method Mathematical and computational analysis focusing on numerical error, computational cost, and stability.
result Explicit answers to fundamental computational issues in shallow networks' high frequency handling.
Corrects gaps in a method for optimizing high-frequency trading strategies.
problem Optimizing bid and ask limit order strategies in high-frequency trading.
method Uses an approximation method based on Avellaneda and Stoikov's 2008 article, correcting gaps found in it.
result The main answer in Avellaneda and Stoikov's article remains unchanged despite corrections.
New method improves Gaussian kernel approximations for high-frequency data.
problem Limited scalability of kernel-based models to large data sets.
method Local random feature approximations using Maclaurin expansions and polynomial sketches.
result Significant improvement in kernel approximations and downstream performance for high-frequency data.
Model-based reinforcement learning has been empirically demonstrated as a successful strategy to improve sample efficiency. In particular, Dyna is an elegant model-based architecture integrating learning and planning that provides huge flexibility of using a model. One of the most important components in Dyna is called…
We conduct a study of the aliased spectral densities of Matérn covariance functions on a regular grid of points, providing clarity on the properties of a popular approximation based on stochastic partial differential equations; while others have shown that it can approximate the covariance function well, we find that i…
In this paper, we provide non-parametric statistical tools to test stationarity of microstructure noise in general hidden Ito semimartingales, and discuss how to measure liquidity risk using high frequency financial data. In particular, we investigate the impact of non-stationary microstructure noise on some volatility…
Study uses multi-kernel Hawkes models to analyze high-frequency price dynamics.
problem Understanding responsive speeds of market participants in high-frequency trading.
method Multi-kernel Hawkes models with conditional Hessian analysis for optimization.
result Existence of multi-kernels (UHF, VHF, HF) in high-frequency price dynamics.
Study optimal liquidation strategies under partial information in high-frequency trading.
problem Optimal liquidation strategies in high-frequency trading with incomplete information.
method Modeling price formation through Hawkes processes, incorporating liquidity as a hidden Markov process, and formulating as an impulse control problem.
result Development of an algorithm to approximate optimal liquidation strategies.
The paper develops a neural network method for estimating drift functions of diffusion processes from discrete observations.
problem Nonparametric estimation of drift function for diffusion processes from high-frequency discrete observations.
method Neural network-based estimator for drift function estimation.
result Derives a non-asymptotic convergence rate for the neural network estimator.
New algorithm trains deep neural networks without global optimization.
problem Training deep neural networks efficiently and without global optimization.
method Uses random complex exponential activation functions and Markov Chain Monte Carlo sampling.
result Consistently attains theoretical approximation rate for residual networks.
DQNs can approximate optimal Q-functions with high accuracy on compact sets.
problem Approximating optimal Q-functions in continuous-time Markov Decision Processes.
method Stochastic control, FBSDEs, residual network approximation theorems, large deviation bounds, viscosity solutions.
result DQNs can approximate optimal Q-functions on compact sets with arbitrary accuracy and high probability.
A new high-frequency market making strategy using Deep Hawkes process.
problem Optimizing high-frequency trading in volatile markets.
method Developed a Deep Hawkes process to model order arrivals and their effects on the limit order book.
result The new strategy outperforms traditional methods in market making.
A compact Riemannian manifold may be immersed into Euclidean space by using high frequency Laplace eigenfunctions. We study the geometry of the manifold viewed as a metric space endowed with the distance function from the ambient Euclidean space. As an application we give a new proof of a result of Burq-Lebeau and othe…
Fast probabilistic option price predictions using modular Bayesian inference.
problem Accurate probabilistic predictions of future option prices.
method Modular approximate Bayesian inference framework that combines multiple data sources.
result Accurate probabilistic option-price predictions in realistic scenarios.
We study tick-by-tick financial returns belonging to the FTSE MIB index of the Italian Stock Exchange (Borsa Italiana). We can confirm previously detected non-stationarities. However, scaling properties reported in the previous literature for other high-frequency financial data are only approximately valid. As a conseq…
HFformer outperforms LSTM in high-frequency trading with multiple signals.
problem Improving high-frequency trading performance using deep learning models.
method Introducing HFformer, a hybrid Transformer model for time series forecasting.
result HFformer achieves higher cumulative PnL than LSTM in backtesting.
We present a novel high frequency residual learning framework, which leads to a highly efficient multi-scale network (MSNet) architecture for mobile and embedded vision problems. The architecture utilizes two networks: a low resolution network to efficiently approximate low frequency components and a high resolution ne…
Study evaluates three ML models for high-frequency trading.
problem Improving accuracy and reliability of high-frequency trading strategies.
method Compared three models: cross-entropy loss + quasi-Newton, FCNN, and vector machine.
result Combination of cross-entropy loss and quasi-Newton outperformed other models.
High-frequency trading strategy boosts battery storage profits.
problem Maximizing revenue for battery energy storage systems in intraday markets.
method Adapted dynamic programming for continuous intraday markets, considering limit order book dynamics.
result Dynamic programming strategy outperforms standard re-optimization methods, increasing profits by 58% and 14% respectively.
A flexible nonparametric online changepoint detection algorithm for high-frequency data.
problem Detecting changes in real-time in high-frequency data streams with limited computational resources.
method NP-FOCuS, a sequential likelihood ratio test for a change in the empirical cumulative density function, using functional pruning.
result NP-FOCuS outperforms current nonparametric online changepoint techniques in various settings.
FFN addresses spectral bias in neural value approximation, improving reinforcement learning performance.
problem Spectral bias in neural value approximation, leading to slow convergence and poor performance.
method Proposes Fourier feature networks (FFN) to overcome spectral bias by using a composite neural tangent kernel.
result FFN achieves state-of-the-art performance on challenging continuous control domains with faster convergence and better stability.
The extremely useful method of Malliavin calculus has not yet gained adequate popularity because of the complicated analytic apparatus of this method. The author attempts here to propose a simplified algebraic formalism similar to Malliavin calculus, but based on the notion of creation-annihilation operators instead of…
We investigated distributions of short term price trends for high frequency stock market data. A number of trends as a function of their lengths was measured. We found that such a distribution does not fit to results following from an uncorrelated stochastic process. We proposed a simple model with a memory that gives …
A new Hawkes process model captures order book dynamics in high-frequency trading.
problem Capturing the complex dynamics of high-frequency trading with large datasets.
method Estimation of an order book dependent Hawkes process using a product of a Hawkes process and covariates.
result Capturing the nonlinearity of order book information improves the model's performance.
New PINN architectures learn high-frequency features using Fourier features.
problem PINNs struggle with high-frequency or multi-scale features.
method Employ spatio-temporal and multi-scale random Fourier features.
result Effective PINN models for multi-scale PDEs.
Informer model with GMADL loss outperforms benchmarks in high frequency Bitcoin trading.
problem Developing automated trading strategies for high frequency Bitcoin data.
method Informer architecture with RMSE, GMADL, and Quantile loss functions.
result Informer model with GMADL loss function outperforms benchmarks in trading outcomes.
FOCuS detects changes in mean from high-frequency data efficiently.
problem Detecting changes in high-frequency data with limited resources.
method FOCuS algorithm that runs multiple window sizes and change sizes simultaneously.
result FOCuS achieves state-of-the-art performance in detecting anomalies.
Proposes a deep RL approach for high-frequency market making using tick data and periodic signals.
problem Challenges in high-frequency market making due to tick-level data complexity and high trading volume.
method Integrates tick-level data with periodic signals using deep reinforcement learning.
result The proposed framework outperforms existing methods in profitability and risk management.
We study a an optimal high frequency trading problem within a market microstructure model designed to be a good compromise between accuracy and tractability. The stock price is driven by a Markov Renewal Process (MRP), while market orders arrive in the limit order book via a point process correlated with the stock pric…
In this paper, we propose a phase shift deep neural network (PhaseDNN) which provides a wideband convergence in approximating a high dimensional function during its training of the network. The PhaseDNN utilizes the fact that many DNN achieves convergence in the low frequency range first, thus, a series of moderately-s…
The paper introduces a new price model based on entropy that better fits high-frequency market data.
problem Understanding fair prices in high-frequency markets with bid-ask imbalance.
method A parametrized family of prices derived from the Maximum Entropy Principle, minimizing bias given volume imbalance.
result The model can generate higher kurtosis and heavy-tailed distributions compared to standard models.
New model reduces volatility parameters and complexity.
problem Accurately modeling multivariate volatility with network structure.
method Introduces a new multivariate volatility model using both low and high-frequency data.
result The model significantly reduces parameter count and computational complexity.
Optimizes trading large volumes of volatile assets with fast mean-reverting volatility.
problem Challenges of executing large volumes of illiquid or volatile assets.
method Modeling uncertain volatility and liquidity with fast mean-reverting dynamics, using singular perturbation arguments and high-frequency data.
result Approximately optimal trade execution strategies under fast mean-reversion.
NBE method speeds up Lévy process parameter estimation.
problem Challenging parameter estimation for Lévy processes with unavailable or costly likelihoods.
method Neural Bayes estimation (NBE) framework using permutation-invariant neural networks.
result NBE provides accurate and consistent estimators with reduced runtime.
FAL improves formation resistivity prediction from cased boreholes with noise resistance.
problem Noise and high-frequency disaster in predicting formation resistivity from cased boreholes.
method Frequency-aware framework and temporal anti-noise block for LSTM.
result FAL achieves a 24.3% improvement in R2 over LSTM, reaching R2=0.91.
We analyze the Gambler's problem, a simple reinforcement learning problem where the gambler has the chance to double or lose the bets until the target is reached. This is an early example introduced in the reinforcement learning textbook by Sutton and Barto (2018), where they mention an interesting pattern of the optim…
Study detects spoofing in high-frequency trading using micro-structural analysis.
problem Challenges in detecting spoofing due to complex electronic platforms and high-frequency trading.
method Micro-structural study in a simplified setting, optimization of spoofing strategy, monitoring with Wasserstein distance.
result Optimal spoofing strategy and its impact on market imbalance quantified.
We derive asymptotic expansions for option data to detect infinite variation volatility.
problem Detecting infinite variation volatility in high-frequency option data.
method Nonparametric higher-order asymptotic expansions for small-time changes of characteristic functions of Itô semimartingales.
result Evidence of infinite variation volatility in high-frequency option data.
The R-function theory of Thomas is used to model neutron inelastic scattering and the fine, intermediate, and gross structure observed in the Dow Jones Industrial Average on a typical trading day.
Estimates drift functions in SDEs using denoising diffusion models.
problem Estimating time-homogeneous drift functions in multivariate SDEs.
method Formulates drift estimation as a denoising problem, trains a conditional diffusion model.
result Proposed estimator matches classical methods in low dimensions and remains competitive in higher dimensions.
GMADL loss function improves model performance and reduces transaction costs.
problem Overfitting and high transaction costs in high-frequency algorithmic trading models.
method Introduces GMADL loss function for better optimization and feature selection.
result GMADL produces superior results and reduces transaction costs compared to standard loss functions.
We build an agent-based model to study how the interplay between low- and high-frequency trading affects asset price dynamics. Our main goal is to investigate whether high-frequency trading exacerbates market volatility and generates flash crashes. In the model, low-frequency agents adopt trading rules based on chronol…
For multi-valued functions---such as when the conditional distribution on targets given the inputs is multi-modal---standard regression approaches are not always desirable because they provide the conditional mean. Modal regression algorithms address this issue by instead finding the conditional mode(s). Most, however,…
This manuscript reports a stochastic dynamical scenario whose associated stationary probability density function is exactly a previously proposed one to adjust high-frequency traded volume distributions. This dynamical conjecture, physically connected to superstatiscs, which is intimately related with the current nonex…