arXiv research

We introduce the class of affine forward variance (AFV) models of which both the conventional Heston model and the rough Heston model are special cases. We show that AFV models can be characterized by the affine form of their cumulant generating function, which can be obtained as solution of a convolution Riccati equat…

The study optimizes bounds for comparing training and population loss.

The paper introduces a new method for detecting financial data outliers.

The paper prices energy spread options using a complex stochastic model.

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

The Heston model is a popular stock price model with stochastic volatility that has found numerous applications in practice. In the present paper, we study the Riemannian distance function associated with the Heston model and obtain explicit formulas for this function using geometrical and analytical methods. Geometric…

We determine the variance-optimal hedge when the logarithm of the underlying price follows a process with stationary independent increments in discrete or continuous time. Although the general solution to this problem is known as backward recursion or backward stochastic differential equation, we show that for this cla…

We consider the performance of non-optimal hedging strategies in exponential Lévy models. Given that both the payoff of the contingent claim and the hedging strategy admit suitable integral representations, we use the Laplace transform approach of Hubalek et al. (2006) to derive semi-explicit formulas for the resulting…

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…

The study analyzes how machine learning classifiers' error rates decrease exponentially based on large deviations theory.

We consider a model for interest rates, where the short rate is given by a time-homogenous, one-dimensional affine process in the sense of Duffie, Filipovic and Schachermayer. We show that in such a model yield curves can only be normal, inverse or humped (i.e. endowed with a single local maximum). Each case can be cha…

Estimates sub-Gaussian parameter with consistent and optimal rates.

Let $σ_t(x)$ denote the implied volatility at maturity $t$ for a strike $K=S_0 e^{xt}$, where $x\in\bbR$ and $S_0$ is the current value of the underlying. We show that $σ_t(x)$ has a uniform (in $x$) limit as maturity $t$ tends to infinity, given by the formula $σ_\infty(x)=\sqrt{2}(h^*(x)^{1/2}+(h^*(x)-x)^{1/2})$, for…

New bounds derived using conditional $f$-information for machine learning models.

This paper sets thresholds for recovering vertex correspondences in partially correlated graphs.

We design and analyze CascadeBAI, an algorithm for finding the best set of $K$ items, also called an arm, within the framework of cascading bandits. An upper bound on the time complexity of CascadeBAI is derived by overcoming a crucial analytical challenge, namely, that of probabilistically estimating the amount of ava…

We investigate the position of the Buchen-Kelly density in a family of entropy maximising densities which all match European call option prices for a given maturity observed in the market. Using the Legendre transform which links the entropy function and the cumulant generating function, we show that it is both the uni…

We present a novel algorithm for overcomplete independent components analysis (ICA), where the number of latent sources k exceeds the dimension p of observed variables. Previous algorithms either suffer from high computational complexity or make strong assumptions about the form of the mixing matrix. Our algorithm does…

Paper improves PAC-Bayes bounds for various loss types.

This paper optimizes importance sampling for rare-event options pricing under the Heston model.

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

New neural network models for complex functional data analysis.

Distance function to a finite set is a topological Morse function.

Introduces new weighted floating functions and affine surface areas.

Develops methods for selecting and estimating smooth functional coefficients in high-dimensional multivariate functional data.

Neural networks can approximate functionals on RKHS with error bounds.

FFBO optimizes functions as inputs and outputs, improving on existing BO methods.

Chirped sinosoids and interferometric phase plots are functions that are not periodic, but are the composition of a smooth function and a periodic function. These functions functions factor into a pair of maps: from their domain to a circle, and from a circle to their codomain. One can easily imagine replacing the circ…

The Fridman function is bounded by the injectivity radius for certain hyperbolic manifolds.

Optimally estimates a functional using nuisance function tuning and sample splitting.

The paper proves isoparametric functions on Finsler space forms under specific conditions.

Paper introduces a nonparametric functional graphical model for random functions.

Robustifies elicitable functionals to handle small distribution misspecifications.

The paper characterizes strong Hamel functions using symmetries and proves their preservation properties.

Study biharmonic functions on vector bundles with spherical symmetry.

Two new methods improve forecasting of functional time series data.

This paper introduces the concept of functional current as a mathematical framework to represent and treat functional shapes, i.e. sub-manifold supported signals. It is motivated by the growing occurrence, in medical imaging and computational anatomy, of what can be described as geometrico-functional data, that is a da…

Study stabilizers of smooth functions on surfaces, focusing on Morse-Bott functions.

The paper connects convex functions to p-subharmonic functions and proves their equivalence.

A new deep neural network tackles nonlinear functional regression with improved dimensionality reduction.

New model for network analysis using functional data.

The study finds a special type of smooth function on connected sums of manifolds.

Function trees simplify complex ML models for better understanding.

We study functions whose truncations are convex or quasiconvex.

NeuTSFlow models continuous functions behind time series forecasting.

New spectral functionals for Dirac operators with inner fluctuations computed.

Regularizers change the geometric properties of loss functions in neural networks.

A new model approximates complex functions in parameter space.