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 establish decoupled functional CLTs for two-time-scale stochastic approximation.
We investigate finite-time decoupled convergence in nonlinear two-time-scale stochastic approximation.
New analysis of stochastic approximation with non-expansive mappings.
Improved bounds for non-linear SA with fast convergence.
Paper analyzes convergence rates of two time-scale AC and NAC algorithms.
This work analyzes actor-critic methods for faster convergence.
Aims to describe neural network training dynamics using two-time-scale models.
We define and discuss the notion of pseudospherical surfaces in asymptotic coordinates on time scales. Two special cases, namely dicrete pseudospherical surfaces and smooth pseudosperical surfaces are consistent with this description. In particular, we define the Gaussian curvature in the discrete case.
In addressing the question of the time scales characteristic for the market formation, we analyze high frequency tick-by-tick data from the NYSE and from the German market. By using returns on various time scales ranging from seconds or minutes up to two days, we compare magnitude of the largest eigenvalue of the corre…
Gradient-based temporal difference (GTD) algorithms are widely used in off-policy learning scenarios. Among them, the two time-scale TD with gradient correction (TDC) algorithm has been shown to have superior performance. In contrast to previous studies that characterized the non-asymptotic convergence rate of TDC only…
The study examines how verifier imperfections impact test-time scaling techniques.
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 …
The paper analyzes Indian stock sectors using multifractal analysis for long and short-term investment.
Circadian rhythms influence multiple essential biological activities including sleep, performance, and mood. The dim light melatonin onset (DLMO) is the gold standard for measuring human circadian phase (i.e., timing). The collection of DLMO is expensive and time-consuming since multiple saliva or blood samples are req…
For the purpose of elucidating the correlation among currencies, we analyze daily and high-resolution data of foreign exchange rates. There is strong correlation for pairs of currencies of geographically near countries. We show that there is a time delay of order less than a minute between two currency markets having a…
New bounds for SA with arbitrary norm contractions and Markovian noise.
In this paper, we study the problems of principal Generalized Eigenvector computation and Canonical Correlation Analysis in the stochastic setting. We propose a simple and efficient algorithm, Gen-Oja, for these problems. We prove the global convergence of our algorithm, borrowing ideas from the theory of fast-mixing M…
Motivated by their broad applications in reinforcement learning, we study the linear two-time-scale stochastic approximation, an iterative method using two different step sizes for finding the solutions of a system of two equations. Our main focus is to characterize the finite-time complexity of this method under time-…
Share price returns on different time scales can be well modelled by a superstatistical dynamics. Here we provide an investigation which type of superstatistics is most suitable to properly describe share price dynamics on various time scales. It is shown that while chi-square superstatistics works well on a time scale…
Different investment strategies are adopted in short-term and long-term depending on the time scales, even though time scales are adhoc in nature. Empirical mode decomposition based Hurst exponent analysis and variance technique have been applied to identify the time scales for short-term and long-term investment from …
We discuss price variations distributions in foreign exchange markets, characterizing them both in calendar and business time frameworks. The price dynamics is found to be the result of two distinct processes, a multi-variance diffusion and an error process. The presence of the latter, which dominates at short time sca…
Atoms and molecules are important conceptual entities we invented to understand the physical world around us. The key to their usefulness lies in the organization of nuclear and electronic degrees of freedom into a single dynamical variable whose time evolution we can better imagine. The use of such effective variables…
We investigate multifractality in the Korean stock-market index KOSPI. The generalized th order height-height correlation function shows multiscaling properties. There are two scaling regimes with a crossover time around min. We consider the original data sets and the modified data sets obtained by removin…
We present for the first time an asymptotic convergence analysis of two time-scale stochastic approximation driven by `controlled' Markov noise. In particular, both the faster and slower recursions have non-additive controlled Markov noise components in addition to martingale difference noise. We analyze the asymptotic…
The correlation matrix is the key element in optimal portfolio allocation and risk management. In particular, the eigenvectors of the correlation matrix corresponding to large eigenvalues can be used to identify the market mode, sectors and style factors. We investigate how these eigenvalues depend on the time scale of…
We define and discuss the notion of pseudospherical surfaces in asymptotic coordinates on time scales. Thus we extend well known notions of discrete pseudospherical surfaces and smooth pseudosperical surfaces on more exotic domains (e.g, the Cantor set). In particular, we present a new expression for the discrete Gauss…
The Empirical Mode Decomposition (EMD) provides a tool to characterize time series in terms of its implicit components oscillating at different time-scales. We apply this decomposition to intraday time series of the following three financial indices: the S\&P 500 (USA), the IPC (Mexico) and the VIX (volatility index US…
We investigate the Heston model with stochastic volatility and exponential tails as a model for the typical price fluctuations of the Brazilian São Paulo Stock Exchange Index (IBOVESPA). Raw prices are first corrected for inflation and a period spanning 15 years characterized by memoryless returns is chosen for the ana…
Financial time series exhibit two different type of non linear correlations: (i) volatility autocorrelations that have a very long range memory, on the order of years, and (ii) asymmetric return-volatility (or `leverage') correlations that are much shorter ranged. Different stochastic volatility models have been propos…
This work explores test-time scaling strategies for LLMs, improving sample efficiency and expressiveness.
The paper studies learning dynamics in two-layer neural networks.
We study two time-scale linear stochastic approximation algorithms, which can be used to model well-known reinforcement learning algorithms such as GTD, GTD2, and TDC. We present finite-time performance bounds for the case where the learning rate is fixed. The key idea in obtaining these bounds is to use a Lyapunov fun…
The paper presents the comparative study of the nature of stock markets in short-term and long-term time scales with and without structural break in the stock data. Structural break point has been identified by applying Zivot and Andrews structural trend break model to break the original time series (TSO) into time ser…
Paper analyzes convergence of two time-scale stochastic approximation using martingale approach.
Q()-Learning improves Q-Learning by separating action-value functions into different time scales.
How can we effectively encode evolving information over dynamic graphs into low-dimensional representations? In this paper, we propose DyRep, an inductive deep representation learning framework that learns a set of functions to efficiently produce low-dimensional node embeddings that evolves over time. The learned embe…
Sharp pseudospectral bounds prevent transient amplification in coupled gradient descent.
We present a simple microstructure model of financial returns that combines (i) the well-known ARFIMA process applied to tick-by-tick returns, (ii) the bid-ask bounce effect, (iii) the fat tail structure of the distribution of returns and (iv) the non-Poissonian statistics of inter-trade intervals. This model allows us…
This work shows how approximate reward models can significantly improve inference-time scaling.
A main theoretical interest in biology and physics is to identify the nonlinear dynamical system (DS) that generated observed time series. Recurrent Neural Networks (RNNs) are, in principle, powerful enough to approximate any underlying DS, but in their vanilla form suffer from the exploding vs. vanishing gradients pro…
Financial markets can be described on several time scales. We use data from the limit order book of the London Stock Exchange (LSE) to compare how the fluctuation dominated microstructure crosses over to a more systematic global behavior.
New method improves likelihood-free parameter estimation in complex models.
We extend and test empirically the multifractal model of asset returns based on a multiplicative cascade of volatilities from large to small time scales. The multifractal description of asset fluctuations is generalized into a multivariate framework to account simultaneously for correlations across times scales and bet…
Study tests rough fractional volatility model across different time scales, revealing new volatility patterns.
Study compares market microstructure between two South African exchanges.
This paper improves traditional Markowitz optimization by considering variance at multiple time scales.
Improved stochastic approximation method reduces residual error.
A digital twin for multi-scale systems uses physics-based and machine learning models.