arXiv research

Volatility roughness studied using fractional noise-driven models.

The study tackles rough noise in high-frequency financial data using fractional Brownian motion.

New framework assesses regularization norms in ill-posed problems, revealing L2 instability and proposing adaptive fractional RKHS solutions.

We develop a variational framework for SDEs driven by fractional noise.

Paper develops Euler scheme for fractional delay diff. eqs with additive noise.

G-framework is presented by Peng [41] for measure risk under uncertainty. In this paper, we define fractional G-Brownian motion (fGBm). Fractional G-Brownian motion is a centered G-Gaussian process with zero mean and stationary increments in the sense of sub-linearity with Hurst index $H\in (0,1)$. This process has sta…

Study confirms rough volatility in financial data, independent of microstructure noise.

We derive an extremal fractional Gaussian by employing the Lévy-Khintchine theorem and Lévian noise. With the fractional Gaussian we then generalize the Black-Scholes-Merton option-pricing formula. We obtain an easily applicable and exponentially convergent option-pricing formula for fractional markets. We also carry o…

Based on empirical market data, a stochastic volatility model is proposed with volatility driven by fractional noise. The model is used to obtain a risk-neutrality option pricing formula and an option pricing equation.

NANSDE-Net models time series with memory using neural ARMA-type noise.

The so-called level crossing analysis has been used to investigate the empirical data set. But there is a lack of interpretation for what is reflected by the level crossing results. The fractional Gaussian noise as a well-defined stochastic series could be a suitable benchmark to make the level crossing findings more s…

Modeling financial markets with memory using fractional calculus and Brownian motion.

Python package for estimating Hurst exponent in fBm.

Based on criteria of mathematical simplicity and consistency with empirical market data, a model with volatility driven by fractional noise has been constructed which provides a fairly accurate mathematical parametrization of the data. Here, some features of the model are discussed and, using agent-based models, one tr…

Study large deviations in fractional volatility models with non-Gaussian volatility.

Based on criteria of mathematical simplicity and consistency with empirical market data, a stochastic volatility model is constructed, the volatility process being driven by fractional noise. Price return statistics and asymptotic behavior are derived from the model and compared with data. Deviations from Black-Scholes…

Paper introduces a new optimization method for imbalanced datasets.

New algorithm robustly learns from corrupted demonstrations, even with constant fraction of noise.

Based on a criterion of mathematical simplicity and consistency with empirical market data, a stochastic volatility model has been obtained with the volatility process driven by fractional noise. Depending on whether the stochasticity generators of log-price and volatility are independent or are the same, two versions …

MAFLA improves sampling from heavy-tailed distributions using MH-inspired corrections.

New neural operators model turbulence with memory and randomness.

Study finds roughness in volatility despite diffusive instantaneous volatility.

We consider the problem of estimating the mean and covariance of a distribution from iid samples in $\mathbb{R}^n$, in the presence of an $η$ fraction of malicious noise; this is in contrast to much recent work where the noise itself is assumed to be from a distribution of known type. The agnostic problem includes many…

We study the problem of robust linear regression with response variable corruptions. We consider the oblivious adversary model, where the adversary corrupts a fraction of the responses in complete ignorance of the data. We provide a nearly linear time estimator which consistently estimates the true regression vector, e…

Based on a criterium of mathematical simplicity and consistency with empirical market data, a stochastic volatility model has been obtained with the volatility process driven by fractional noise. Depending on whether the stochasticity generators of log-price and volatility are independent or are the same, two versions …

New RDP guarantees for heavy-tailed SDEs and SGD.

New model captures long-term memory effects in epidemic dynamics.

The paper proposes estimators for bid-ask spreads with and without serial dependence.

Enhanced financial forecasting using supervised autoencoders with noise augmentation and triple labeling.

We consider the problem of estimating the support of a vector $β^* \in \mathbb{R}^{p}$ based on observations contaminated by noise. A significant body of work has studied behavior of $\ell_1$-relaxations when applied to measurement matrices drawn from standard dense ensembles (e.g., Gaussian, Bernoulli). In this paper,…

Recent studies on diffusion-based sampling methods have shown that Langevin Monte Carlo (LMC) algorithms can be beneficial for non-convex optimization, and rigorous theoretical guarantees have been proven for both asymptotic and finite-time regimes. Algorithmically, LMC-based algorithms resemble the well-known gradient…

Composite likelihood inference of fractional Gaussian processes with sequentially optimal subset selection

Image reconstruction in low-count PET is particularly challenging because gammas from natural radioactivity in Lu-based crystals cause high random fractions that lower the measurement signal-to-noise-ratio (SNR). In model-based image reconstruction (MBIR), using more iterations of an unregularized method may increase t…

Quantum probability theory constructs Martingales for non-Brownian financial models.

We study fractional stochastic volatility models in which the volatility process is a positive continuous function $σ$ of a continuous Gaussian process $\widehat{B}$. Forde and Zhang established a large deviation principle for the log-price process in such a model under the assumptions that the function $σ$ is globally…

This work obtains novel finite sample guarantees for Principal Component Analysis (PCA). These hold even when the corrupting noise is non-isotropic, and a part (or all of it) is data-dependent. Because of the latter, in general, the noise and the true data are correlated. The results in this work are a significant impr…

We consider the problem of reconstructing a low rank matrix from noisy observations of a subset of its entries. This task has applications in statistical learning, computer vision, and signal processing. In these contexts, "noise" generically refers to any contribution to the data that is not captured by the low-rank m…

fSDE-Net generates time series with long-term memory using neural networks.

Adversarial inference on tree models is possible with limited corruption, improving on Kesten-Stigum threshold.

We consider the non-parametric regression problem under Huber's $ε$-contamination model, in which an $ε$ fraction of observations are subject to arbitrary adversarial noise. We first show that a simple local binning median step can effectively remove the adversary noise and this median estimator is minimax optimal up t…

The paper establishes risk bounds for PU learning with label noise.

Adaptive Langevin dynamics reduces bias in Bayesian inference with mini-batching.

In this paper, the Kyle model of insider trading is extended by characterizing the trading volume with long memory and allowing the noise trading volatility to follow a general stochastic process. Under this newly revised model, the equilibrium conditions are determined, with which the optimal insider trading strategy,…

We consider rough stochastic volatility models where the driving noise of volatility has fractional scaling, in the "rough" regime of Hurst parameter $H < 1/2$. This regime recently attracted a lot of attention both from the statistical and option pricing point of view. With focus on the latter, we sharpen the large de…

Noisy PN learning is the problem of binary classification when training examples may be mislabeled (flipped) uniformly with noise rate rho1 for positive examples and rho0 for negative examples. We propose Rank Pruning (RP) to solve noisy PN learning and the open problem of estimating the noise rates, i.e. the fraction …

Framework for fair classification with noisy protected attributes and provable guarantees.

A method for estimating parameters from entangled single-sample distributions, robust to high-noise data.

Algorithm learns halfspaces in noisy data efficiently.