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.
Study mass transport in low-diffusivity using Lagrangian coordinates.
New risk bound for drift estimator in stochastic models.
The time average of geometric Brownian motion plays a crucial role in the pricing of Asian options in mathematical finance. In this paper we consider the asymptotics of the discrete-time average of a geometric Brownian motion sampled on uniformly spaced times in the limit of a very large number of averaging time steps.…
New method for unbiased regression reduces excess risk.
We analyze the question whether sliding window time averages applied to stationary increment processes converge to a limit in probability. The question centers on averages, correlations, and densities constructed via time averages of the increment x(t,T)=x(t+T)-x(t)and the assumption is that the increment is distribute…
Derives time-averaged active inference from control principles.
The paper analyzes sampling and estimation on manifolds using Langevin diffusion.
In modern portfolio theory, the balancing of expected returns on investments against uncertainties in those returns is aided by the use of utility functions. The Kelly criterion offers another approach, rooted in information theory, that always implies logarithmic utility. The two approaches seem incompatible, too loos…
Geometric Brownian motion (GBM) is a model for systems as varied as financial instruments and populations. The statistical properties of GBM are complicated by non-ergodicity, which can lead to ensemble averages exhibiting exponential growth while any individual trajectory collapses according to its time-average. A com…
Paper proposes a mean-field gradient descent for zero-sum games, proving convergence to Nash equilibrium.
We revisit and demonstrate the Epps effect using two well-known non-parametric covariance estimators; the Malliavin and Mancino (MM), and Hayashi and Yoshida (HY) estimators. We show the existence of the Epps effect in the top 10 stocks from the Johannesburg Stock Exchange (JSE) by various methods of aggregating Trade …
Since the pioneering work of Ghys, Langevin and Walczak among others, it has been known that several methods of dynamical systems theory can be adopted to study of foliations. Our aim in this paper is to investigate complexity of foliations, by generalising existence problem of time averages in dynamical systems theory…
Voluntary insurance contracts constitute a puzzle because they increase the expectation value of one party's wealth, whereas both parties must sign for such contracts to exist. Classically, the puzzle is resolved by introducing non-linear utility functions, which encode asymmetric risk preferences; or by assuming the p…
We provide a surprising new application of classical approximation theory to a fundamental asset-pricing model of mathematical finance. Specifically, we calculate an analytic value for the correlation coefficient between exponential Brownian motion and its time average, and we find the use of divided differences greatl…
The paper develops a new theory to understand deep learning optimization.
Enhances UPSA to reduce noise in financial data.
The definition of the covariant space-time averaging scheme for the objects (tensors, geometric objects, etc.) on differentiable metric manifolds with a volume n-form, which has been proposed for the formulation of macroscopic gravity, is analyzed. An overview of the space-time averaging procedure in Minkowski spacetim…
A new MFG framework for evolving clusters from Gaussian mixtures.
We give a new proof of the representation of implied volatility as a time-average of weighted expectations of local or stochastic volatility. With this proof we clarify the question of existence of 'forward implied variance' in the original derivation of Gatheral, who introduced this representation in his book 'The Vol…
A graph homomorphism is a map between two graphs that preserves adjacency relations. We consider the problem of sampling a random graph homomorphism from a graph into a large network. We propose two complementary MCMC algorithms for sampling random graph homomorphisms and establish bounds on their mixing times and the …
A resolution of the St. Petersburg paradox is presented. In contrast to the standard resolution, utility is not required. Instead, the time-average performance of the lottery is computed. The final result can be phrased mathematically identically to Daniel Bernoulli's resolution, which uses logarithmic utility, but is …
The paper introduces Robust Correlated Equilibrium for games with time-varying costs and proposes an algorithm to achieve it.
We present a rigorous study of the short maturity asymptotics for Asian options with continuous-time averaging, under the assumption that the underlying asset follows the Constant Elasticity of Variance (CEV) model. We present an analytical approximation for the Asian options prices which has the appropriate short matu…
We consider the problem of tracking a target whose dynamics is modeled by a continuous Itō semi-martingale. The aim is to minimize both deviation from the target and tracking efforts. We establish the existence of asymptotic lower bounds for this problem, depending on the cost structure. These lower bounds can be relat…
We study the price dynamics of stocks traded in the NASDAQ market by considering the statistical properties of an ensemble of stocks traded simultaneously. For each trading day of our database, we study the ensemble return distribution by extracting its first two central moments. According to previous results obtained …
We study the non-stationary stochastic multiarmed bandit (MAB) problem and propose two generic algorithms, namely, the limited memory deterministic sequencing of exploration and exploitation (LM-DSEE) and the Sliding-Window Upper Confidence Bound# (SW-UCB#). We rigorously analyze these algorithms in abruptly-changing a…
This paper analyzes popular time-nonseparable utility functions that describe "habit formation" consumer preferences comparing current consumption with the time averaged past consumption of the same individual and "catching up with the Joneses" (CuJ) models comparing individual consumption with a cross-sectional averag…
We study the asymptotic behavior of distribution densities arising in stock price models with stochastic volatility. The main objects of our interest in the present paper are the density of time averages of the squared volatility process and the density of the stock price process in the Stein-Stein and the Heston model…
Ridge regression linked to Poisson resetting in statistical physics.
AdaBoost is one of the most popular ML algorithms. It is simple to implement and often found very effective by practitioners, while still being mathematically elegant and theoretically sound. AdaBoost's interesting behavior in practice still puzzles the ML community. We address the algorithm's stability and establish m…
We study the multi-player stochastic multiarmed bandit (MAB) problem in an abruptly changing environment. We consider a collision model in which a player receives reward at an arm if it is the only player to select the arm. We design two novel algorithms, namely, Round-Robin Sliding-Window Upper Confidence Bound\# (RR-…
We present a rigorous study of the short maturity asymptotics for Asian options with continuous-time averaging, under the assumption that the underlying asset follows a local volatility model. The asymptotics for out-of-the-money, in-the-money, and at-the-money cases are derived, considering both fixed strike and float…
Study finds a small correction to Asian option volatility.
In distributed reinforcement learning, it is common to exchange the experience memory of each agent and thereby collectively train their local models. The experience memory, however, contains all the preceding state observations and their corresponding policies of the host agent, which may violate the privacy of the ag…
Logarithmic regret for continuous-time reinforcement learning.
Ordinary stochastic neural networks mostly rely on the expected values of their weights to make predictions, whereas the induced noise is mostly used to capture the uncertainty, prevent overfitting and slightly boost the performance through test-time averaging. In this paper, we introduce variance layers, a different k…
Automates learning of multivariate diffusions for generative models.
Masking diffusion outperforms other discrete diffusion models by incorporating jump times into the model.
Diffusion-GAN uses diffusion to improve GAN training stability and realism.
Study shows how heat leaks from material sets in low diffusivity scenarios.
New blurring diffusion models bridge heat dissipation and denoising.
Based on the tick-by-tick price changes of the companies from the U.S. and from the German stock markets over the period 1998-99 we reanalyse several characteristics established by the Boston Group for the U.S. market in the period 1994-95, which serves to verify their space and time-translational invariance. By increa…
New method tackles video inverse problems using image diffusion models.
Diffusion models generate new samples with active guidance, but theory is limited.
Unified framework for multi-view diffusion geometries using intertwined diffusion trajectories.
PaGoDA reduces diffusion model training costs by 64x.
Study shows diffused interface flows to single diffused balls over time.
Latent diffusion improves robustness in missing data imputation.