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.
Develops a martingale expansion for stochastic volatility models.
New statistical inference method for high-dimensional Hawkes processes.
We give concentration bounds for martingales that are uniform over finite times and extend classical Hoeffding and Bernstein inequalities. We also demonstrate our concentration bounds to be optimal with a matching anti-concentration inequality, proved using the same method. Together these constitute a finite-time versi…
The information dynamics in finance and insurance applications is usually modeled by a filtration. This paper looks at situations where information restrictions apply such that the information dynamics may become non-monotone. A fundamental tool for calculating and managing risks in finance and insurance are martingale…
Paper analyzes CLT for TTSA with Markovian noise, broadening its applications.
We provide non-asymptotic convergence rates of the Polyak-Ruppert averaged stochastic gradient descent (SGD) to a normal random vector for a class of twice-differentiable test functions. A crucial intermediate step is proving a non-asymptotic martingale central limit theorem (CLT), i.e., establishing the rates of conve…
We establish decoupled functional CLTs for two-time-scale stochastic approximation.
Study bounds noise level in linear regression with dependent data.
Existence proved for -Bass martingales with specific marginals.
The paper analyzes Q-learning convergence rates with asynchronous updates.
Proposes a new algorithm to estimate invariant subspaces across multilayer networks.
The paper develops a method for self-normalized inference in adaptive experiments.
In this paper, we study the Edgeworth expansion for a pre-averaging estimator of quadratic variation in the framework of continuous diffusion models observed with noise. More specifically, we obtain a second order expansion for the joint density of the estimators of quadratic variation and its asymptotic variance. Our …
In this paper, we obtain stability results for martingale representations in a very general framework. More specifically, we consider a sequence of martingales each adapted to its own filtration, and a sequence of random variables measurable with respect to those filtrations. We assume that the terminal values of the m…
Study shows how market firm capitalization models converge to stochastic PDE solutions.
The paper reviews historical and modern approaches to asset pricing probability measures.
The paper studies reward concentration in MDPs, covering asymptotic and non-asymptotic settings.
FMP sampling improves model calibration without sharing data.
Martingale Doppelgänger-Eval benchmarks VLMs on candlestick evidence vs. trend extrapolation
Without probability theory, we define classes of supermartingales, martingales, and semimartingales in idealized financial markets with continuous price paths. This allows us to establish probability-free versions of a number of standard results in martingale theory, including the Dubins-Schwarz theorem, the Girsanov t…
This paper is concerned with the estimation of the volatility process in a stochastic volatility model of the following form: , where denotes the log-price and is a càdlàg semi-martingale. In the spirit of a series of recent works on the estimation of the cumulated volatility, we here focus …
We win EVA2025 by estimating extreme precipitation events using Peaks Over Thresholds and martingale testing.
We propose procedures for testing whether stock price processes are martingales based on limit order type betting strategies. We first show that the null hypothesis of martingale property of a stock price process can be tested based on the capital process of a betting strategy. In particular with high frequency Markov …
Estimators computed from adaptively collected data do not behave like their non-adaptive brethren. Rather, the sequential dependence of the collection policy can lead to severe distributional biases that persist even in the infinite data limit. We develop a general method -- -decorrelation -- for transformi…
We present a set of high-probability inequalities that control the concentration of weighted averages of multiple (possibly uncountably many) simultaneously evolving and interdependent martingales. Our results extend the PAC-Bayesian analysis in learning theory from the i.i.d. setting to martingales opening the way for…
We put forward a complete theory on moment explosion for fairly general state-spaces. This includes a characterization of the validity of the affine transform formula in terms of minimal solutions of a system of generalized Riccati differential equations. Also, we characterize the class of positive semidefinite process…
A concept of martingale-fair index of return, consistent with Arbitrage Free Pricing Theory, is introduced. An explicit formula for the average rate of return of a group of investment/pension funds in a discrete time stochastic model is derived and several properties of this index are shown. In particular, it is proven…
Paper defines saddle points in asymmetric Dynkin games using martingale theory.
In the framework of bilateral Gamma stock models we seek for adequate option pricing measures, which have an economic interpretation and allow numerical calculations of option prices. Our investigations encompass Esscher transforms, minimal entropy martingale measures, -optimal martingale measures, bilateral Esscher…
MOSAIC detects change points in dynamic networks with low-rank and sparse changes.
In this work, we propose an algorithm to price American options by directly solving the dual minimization problem introduced by Rogers. Our approach relies on approximating the set of uniformly square integrable martingales by a finite dimensional Wiener chaos expansion. Then, we use a sample average approximation tech…
The paper derives the QGS equations using stochastic central extensions.
Study uniform learnability of binary classification networks with communication.
Recurrent neural networks' hidden state can be reconstructed from its past, providing a theoretical framework for stability and tracking.
Study random walks on groups with superlinear divergent geodesics.
Extends specific relative entropy to multidimensional continuous martingales.
We prove that, for locally bounded processes, absence of arbitrage opportunities of the first kind is equivalent to the existence of a dominating local martingale measure. This is related to and motivated by results from the theory of filtration enlargements.
New method finds closest martingale to Brownian motion.
Score-based martingale posteriors improve uncertainty quantification in deep neural networks.
New approach shows continuity and compactness of martingale measures.
The main result of this paper that a martingale evolution can be chosen for Libor such that all the Libor interest rates have a common market measure; the drift is fixed such that each Libor has the martingale property. Libor is described using a field theory model, and a common measure is seen to be emerge naturally f…
Geometric Bass martingales linked to Brownian motion and geometric Brownian motion.
Modeling the evolution of a financial index as a stochastic process is a problem awaiting a full, satisfactory solution since it was first formulated by Bachelier in 1900. Here it is shown that the scaling with time of the return probability density function sampled from the historical series suggests a successful mode…
The paper connects neural networks to physics using probability theory.
As relational datasets modeled as graphs keep increasing in size and their data-acquisition is permeated by uncertainty, graph-based analysis techniques can become computationally and conceptually challenging. In particular, node centrality measures rely on the assumption that the graph is perfectly known -- a premise …
Quantum probability theory constructs Martingales for non-Brownian financial models.
Study scaling limits of utility indifference prices in discretized Bachelier model.
We introduce a new class of processes for the evaluation of multivariate equity derivatives. The proposed setting is well suited for the application of the standard copula function theory to processes, rather than variables, and easily enables to enforce the martingale pricing requirement. The martingale condition is i…