arXiv research

Study quantifies how LLMs capture higher-order statistical structure using cumulant expansion.

Cumulant expansion is used to derive accurate closed-form approximation for Monthly Sum Options in case of constant volatility model. Payoff of Monthly Sum Option is based on sum of $N$ caped (and probably floored) returns. It is noticed, that $1/\sqrt{N}$ can be used as a small parameter in Edgeworth expansion. First …

The paper provides non-asymptotic Edgeworth expansions for neural network outputs.

Motivated by the need for parametric families of rich and yet tractable distributions in financial mathematics, both in pricing and risk management settings, but also considering wider statistical applications, we investigate a novel technique for introducing skewness or kurtosis into a symmetric or other distribution.…

Study asymptotic properties of generalized shortfall risk measures for heavy-tailed risks.

The paper revisits expected signatures in semimartingale models, providing new formulae and simplifying complexity.

We obtain a first order extension of the large deviation estimates in the Gärtner-Ellis theorem. In addition, for a given family of measures, we find a special family of functions having a similar Laplace principle expansion up to order one to that of the original family of measures. The construction of the special fam…

We analyze the semi-hard triplet loss using Edgeworth expansion for better understanding of its behavior.

Refining a discrete model of Cheuk and Vorst we obtain a closed formula for the price of a European lookback option at any time between emission and maturity. We derive an asymptotic expansion of the price as the number of periods tends to infinity, thereby solving a problem posed by Lin and Palmer. We prove, in partic…

Estimates MLP expected output without sampling, using fewer FLOPs.

New COS method formula improves option pricing accuracy.

We derive a new, exact and transparent expansion for option smiles, which lends itself both to analytical approximation and, perhaps more importantly, to congenial numerical treatments. We show that the skew and the curvature of the smile can be computed as exotic options, for which the Hedged Monte Carlo method is par…

We study the impact of learning on the optimal policy and the time-to-decision in an infinite-horizon Bayesian sequential decision model with two irreversible alternatives, exit and expansion. In our model, a firm undertakes a small-scale pilot project so as to learn, via Bayesian updating, about the project\textquoter…

Bayesian optimisation algorithm for unknown search spaces with sub-linear regret.

In this work we present an analytical model, based on the path-integral formalism of Statistical Mechanics, for pricing options using first-passage time problems involving both fixed and deterministically moving absorbing barriers under possible non-gaussian distributions of the underlying object. We adapt to our probl…

Developing a differentially private deep learning algorithm is challenging, due to the difficulty in analyzing the sensitivity of objective functions that are typically used to train deep neural networks. Many existing methods resort to the stochastic gradient descent algorithm and apply a pre-defined sensitivity to th…

Study spectral density of neural networks using resolvent method.

Expectation Propagation (EP) provides a framework for approximate inference. When the model under consideration is over a latent Gaussian field, with the approximation being Gaussian, we show how these approximations can systematically be corrected. A perturbative expansion is made of the exact but intractable correcti…

New tensor framework connects Fisher information, hypergraphs, and multi-observable correlations.

This study provides an explicit expansion of KL divergence's gradient flow in Fisher-Rao geometry.

Study proposes a new model for joint survival annuity valuation.

Refines online learning to rank algorithm with tighter bounds.

Paper introduces a new method for efficient portfolio risk quantification.

Study examines short-term IVS dynamics using a model-independent approach.

A new PCA method for analyzing point processes.

Study of correlated Wigner matrices with BBP transitions.

We deal with the efficient parallelization of Bayesian global optimization algorithms, and more specifically of those based on the expected improvement criterion and its variants. A closed form formula relying on multivariate Gaussian cumulative distribution functions is established for a generalized version of the mul…

Uniform heat kernel and diffusion bridge asymptotics for sub-Riemannian geometry.

The CSA-ES is an Evolution Strategy with Cumulative Step size Adaptation, where the step size is adapted measuring the length of a so-called cumulative path. The cumulative path is a combination of the previous steps realized by the algorithm, where the importance of each step decreases with time. This article studies …

Using methods introduced by Scargle in 1978 we derive a cumulative version of the Lomb periodogram that exhibits frequency independent statistics when applied to cumulative noise. We show how this cumulative Lomb periodogram allows us to estimate the significance of log-periodic signatures in the S&P 500 anti-bubble th…

Generative model for condensed matter using Riemannian flow matching.

Kernel for Lévy rough paths derived from PDE system.

Kernelized cumulants improve statistical analysis in high-dimensional spaces.

Neural networks can learn from higher-order cumulants efficiently, requiring quadratic samples.

A new GAN loss function based on cumulant generating functions improves stability and robustness.

The paper calculates bounds for risk metrics and entropies under partial information constraints.

The parametric complexity is the key quantity in the minimum description length (MDL) approach to statistical model selection. Rissanen and others have shown that the parametric complexity of a statistical model approaches a simple function of the Fisher information volume of the model as the sample size $n$ goes to in…

Bayesian methods improve inference for cumulative probit models on large datasets.

The problem of an arbitrary truncated Levy flight description using the method of cumulant approach has been solved. The set of cumulants of the truncated Levy distribution given the assumption of arbitrary truncation has been found. The influence of truncation shape on the truncated Levy flight properties in the Gauss…

Rescaling expansiveness proven for k*-expansive vector fields.

CENNSurv models cumulative effects of time-dependent exposures on survival outcomes.

The paper derives expansions for Green's operators and resolvents using Hadamard methods.

New algorithms minimize simple and cumulative regret in contextual bandits.

Method determines credit transition matrix from cumulative default probabilities.

New method calibrates classifier probabilities with guaranteed coverage.

Paper converts quantiles to cumulative distribution functions to simplify risk measures.

We introduce a new type of graphical model called a "cumulative distribution network" (CDN), which expresses a joint cumulative distribution as a product of local functions. Each local function can be viewed as providing evidence about possible orderings, or rankings, of variables. Interestingly, we find that the condi…

Develops regression trees for estimating cumulative incidence curves in competing risks.