arXiv subjects

Ruixun Zhang

Publications and source records attributed to Ruixun Zhang.

12 recordsLinked to original sources

arXiv2026

How Fast Do Signatures Learn? Statistical Theory and Applications for Path Regression

Many prediction and decision-making problems in operations research involve path-valued covariates -- data that evolve over time -- for which path signatures have become a canonical feature representation. Their use is justified by a universal approximation theorem, but this is an existence result: it guarantees that a finite-level signature can approximate any continuous path functional, without quantifying how fast the approximation error decreases as the truncation level grows. This paper develops approximation and statistical theory for signature-based path regression. We establish an \(L^2\) approximation rate for smooth functionals of It\^{o} diffusions and show that it is minimax optimal. We then propagate the truncation error through three statistical learning procedures -- Signature-OLS, Signature-LASSO, and Signature-Logistic -- and establish their consistency. Three real-data applications show that signatures provide informative finite-dimensional representations of path-valued covariates and can improve prediction relative to handcrafted features, in the context of finance -- foreign exchange realized volatility forecasting from intraday price paths; energy -- battery end-of-life prediction from early diagnostic current-voltage pulse paths; and medicine -- epileptic seizure detection from short electroencephalogram windows.

math.ST↗

arXiv2026

Tradable It\^o Signatures: A Model-Free, Interpretable Framework for Dynamic Hedging

We propose an interpretable machine-learning framework for dynamic hedging using the It\^o signature transform, which turns asset-price paths into a set of linear features that universally represent nonlinear functions on time-series. We show that each discretized It\^o signature component can be perfectly replicated by a simple self-financing strategy using only the underlying assets and cash, which turns It\^o signature components into tradable and transparent hedging bases. This allows nonlinear derivative payoffs to be approximated by linear combinations of signature terms and hedged through the corresponding combination of trading strategies. We further establish a new approximation result for the It\^o signature and derive theoretical bounds for both in-sample and out-of-sample hedging errors. Our method is computationally efficient, easy to implement, and avoids the estimation of future conditional expectations, which makes it attractive for real-world applications. In simulations, our method delivers strong sample efficiency at substantially lower computational cost than neural-network benchmarks. In an empirical study of S\&P 500 index options, it performs robustly across vanilla and path-dependent contracts, with the signature-kernel weighted version providing further gains by localizing estimation to similar historical market paths. Overall, the paper identifies the It\^o signature as a practical, transparent, and model-agnostic implementation framework for dynamic hedging.

q-fin.CP↗

arXiv2026

Scalable Bi-causal Optimal Transport via KL Relaxation and Policy Gradients

Bi-causal optimal transport (OT) is a natural framework for comparing and coupling stochastic processes under nonanticipative information constraints, with important applications in robust finance, sequential uncertainty quantification, and multistage stochastic optimization. In particular, a learned bi-causal coupling naturally serves as a simulator for generating joint sample paths that respect both prescribed marginal laws and the underlying information flow. Its practical use, however, is limited by the computational difficulty of enforcing bi-causal coupling constraints over path space, especially for continuous distributions and long horizons. We develop a scalable stochastic-optimization framework for computing bi-causal OT couplings under general marginals. Our approach introduces a Kullback--Leibler (KL)-penalized relaxation that replaces hard marginal constraints with tractable divergence penalties while preserving the recursive structure of the problem. We establish dynamic programming principles for both the original and relaxed formulations, prove that the relaxed problem converges to the original bi-causal OT problem as the penalty grows, and derive explicit policy-gradient representations for the relaxed objective. Building on these results, we propose a practical policy-gradient algorithm with unbiased mini-batch estimators, variance reduction, and nonasymptotic regret guarantees. Numerical experiments show that the method accurately captures marginal laws and temporal dependence, and performs well in applications including robust subhedging and time series statistical downscaling. These results provide a scalable computational approach to bi-causal OT and broaden its applicability in settings where nonanticipative information constraints are essential.

math.OC↗

arXiv2025

FinFlowRL: An Imitation-Reinforcement Learning Framework for Adaptive Stochastic Control in Finance

Traditional stochastic control methods in finance rely on simplifying assumptions that often fail in real world markets. While these methods work well in specific, well defined scenarios, they underperform when market conditions change. We introduce FinFlowRL, a novel framework for financial stochastic control that combines imitation learning with reinforcement learning. The framework first pretrains an adaptive meta policy by learning from multiple expert strategies, then finetunes it through reinforcement learning in the noise space to optimize the generation process. By employing action chunking, that is generating sequences of actions rather than single decisions, it addresses the non Markovian nature of financial markets. FinFlowRL consistently outperforms individually optimized experts across diverse market conditions.

q-fin.CP↗

arXiv2025

Convergence Rate in Nonlinear Two-Time-Scale Stochastic Approximation with State (Time)-Dependence

The nonlinear two-time-scale stochastic approximation is widely studied under conditions of bounded variances in noise. Motivated by recent advances that allow for variability linked to the current state or time, we consider state- and time-dependent noises. We show that the Lyapunov function exhibits polynomial convergence rates in both cases, with the rate of polynomial delay depending on the parameters of state- or time-dependent noises. Notably, if the state noise parameters fully approach their limiting value, the Lyapunov function achieves an exponential convergence rate. We provide two numerical examples to illustrate our theoretical findings in the context of stochastic gradient descent with Polyak-Ruppert averaging and stochastic bilevel optimization.

math.OC↗

arXiv2025

Diffusion Factor Models: Generating High-Dimensional Returns with Factor Structure

Financial scenario simulation is essential for risk management and portfolio optimization, yet it remains challenging especially in high-dimensional and small data settings common in finance. We propose a diffusion factor model that integrates latent factor structure into generative diffusion processes, bridging econometrics with modern generative AI to address the challenges of the curse of dimensionality and data scarcity in financial simulation. By exploiting the low-dimensional factor structure inherent in asset returns, we decompose the score function--a key component in diffusion models--using time-varying orthogonal projections, and this decomposition is incorporated into the design of neural network architectures. We derive rigorous statistical guarantees, establishing nonasymptotic error bounds for both score estimation at O(d^{5/2} n^{-2/(k+5)}) and generated distribution at O(d^{5/4} n^{-1/2(k+5)}), primarily driven by the intrinsic factor dimension k rather than the number of assets d, surpassing the dimension-dependent limits in the classical nonparametric statistics literature and making the framework viable for markets with thousands of assets. Numerical studies confirm superior performance in latent subspace recovery under small data regimes. Empirical analysis demonstrates the economic significance of our framework in constructing mean-variance optimal portfolios and factor portfolios. This work presents the first theoretical integration of factor structure with diffusion models, offering a principled approach for high-dimensional financial simulation with limited data. Our code is available at https://github.com/xymmmm00/diffusion_factor_model.

q-fin.ST↗

arXiv2024

Debiasing Watermarks for Large Language Models via Maximal Coupling

Watermarking language models is essential for distinguishing between human and machine-generated text and thus maintaining the integrity and trustworthiness of digital communication. We present a novel green/red list watermarking approach that partitions the token set into ``green'' and ``red'' lists, subtly increasing the generation probability for green tokens. To correct token distribution bias, our method employs maximal coupling, using a uniform coin flip to decide whether to apply bias correction, with the result embedded as a pseudorandom watermark signal. Theoretical analysis confirms this approach's unbiased nature and robust detection capabilities. Experimental results show that it outperforms prior techniques by preserving text quality while maintaining high detectability, and it demonstrates resilience to targeted modifications aimed at improving text quality. This research provides a promising watermarking solution for language models, balancing effective detection with minimal impact on text quality.

stat.ML↗

arXiv2024

Periodic Trading Activities in Financial Markets: Mean-field Liquidation Game with Major-Minor Players

Motivated by recent empirical findings on the periodic phenomenon of aggregated market volumes in equity markets, we aim to understand the causes and consequences of periodic trading activities through a game-theoretic perspective, examining market interactions among different types of participants. Specifically, we introduce a new mean-field liquidation game involving major and minor traders, where the major trader evaluates her strategy against a periodic targeting strategy while a continuum of minor players trade against her. We establish the existence and uniqueness of an open-loop Nash equilibrium. In addition, we prove an O(1/sqrt N) approximation rate of the mean-field solution to the Nash equilibrium in a major-minor game with N minor players. In equilibrium, minor traders exhibit front-running behaviors in both the periodic and trend components of their strategies, reducing the major trader's profit. Such strategic interactions diminish the strength of periodicity in both overall trading volume and asset prices. Our model rationalizes observed periodic trading activities in the market and offers new insights into market dynamics.

q-fin.MF↗

arXiv2024

The checkerboard copula and dependence concepts

We study the problem of choosing the copula when the marginal distributions of a random vector are not all continuous. Inspired by four motivating examples including simulation from copulas, stress scenarios, co-risk measures, and dependence measures, we propose to use the checkerboard copula, that is, intuitively, the unique copula with a distribution that is as uniform as possible within regions of flexibility. We show that the checkerboard copula has the largest Shannon entropy, which means that it carries the least information among all possible copulas for a given random vector. Furthermore, the checkerboard copula preserves the dependence information of the original random vector, leading to two applications in the context of diversification penalty and impact portfolios. The numerical and empirical results illustrate the benefits of using the checkerboard copula in the calculation of co-risk measures.

q-fin.RM↗

arXiv2024

The Devil is in the Details: Boosting Guided Depth Super-Resolution via Rethinking Cross-Modal Alignment and Aggregation

Guided depth super-resolution (GDSR) involves restoring missing depth details using the high-resolution RGB image of the same scene. Previous approaches have struggled with the heterogeneity and complementarity of the multi-modal inputs, and neglected the issues of modal misalignment, geometrical misalignment, and feature selection. In this study, we rethink some essential components in GDSR networks and propose a simple yet effective Dynamic Dual Alignment and Aggregation network (D2A2). D2A2 mainly consists of 1) a dynamic dual alignment module that adapts to alleviate the modal misalignment via a learnable domain alignment block and geometrically align cross-modal features by learning the offset; and 2) a mask-to-pixel feature aggregate module that uses the gated mechanism and pixel attention to filter out irrelevant texture noise from RGB features and combine the useful features with depth features. By combining the strengths of RGB and depth features while minimizing disturbance introduced by the RGB image, our method with simple reuse and redesign of basic components achieves state-of-the-art performance on multiple benchmark datasets. The code is available at https://github.com/JiangXinni/D2A2.

cs.CV↗

arXiv2023

On Consistency of Signature Using Lasso

Signatures are iterated path integrals of continuous and discrete-time processes, and their universal nonlinearity linearizes the problem of feature selection in time series data analysis. This paper studies the consistency of signature using Lasso regression, both theoretically and numerically. We establish conditions under which the Lasso regression is consistent both asymptotically and in finite sample. Furthermore, we show that the Lasso regression is more consistent with the It\^o signature for time series and processes that are closer to the Brownian motion and with weaker inter-dimensional correlations, while it is more consistent with the Stratonovich signature for mean-reverting time series and processes. We demonstrate that signature can be applied to learn nonlinear functions and option prices with high accuracy, and the performance depends on properties of the underlying process and the choice of the signature.

stat.ML↗

arXiv2021

M2RNet: Multi-modal and Multi-scale Refined Network for RGB-D Salient Object Detection

Salient object detection is a fundamental topic in computer vision. Previous methods based on RGB-D often suffer from the incompatibility of multi-modal feature fusion and the insufficiency of multi-scale feature aggregation. To tackle these two dilemmas, we propose a novel multi-modal and multi-scale refined network (M2RNet). Three essential components are presented in this network. The nested dual attention module (NDAM) explicitly exploits the combined features of RGB and depth flows. The adjacent interactive aggregation module (AIAM) gradually integrates the neighbor features of high, middle and low levels. The joint hybrid optimization loss (JHOL) makes the predictions have a prominent outline. Extensive experiments demonstrate that our method outperforms other state-of-the-art approaches.

cs.CV↗