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.
Proposes a new classification model using extended exponential functions.
A new model relaxes constraints on exponential dispersion models.
In this paper, we study the dividend strategies for a shareholder with non-constant discount rate in a diffusion risk model. We assume that the dividends can only be paid at a bounded rate and restrict ourselves to the Markov strategies. This is a time inconsistent control problem. The extended HJB equation is given an…
New theory extends LQ control to non-exponential discount scenarios.
Classification is the most important process in data analysis. However, due to the inherent non-convex and non-smooth structure of the zero-one loss function of the classification model, various convex surrogate loss functions such as hinge loss, squared hinge loss, logistic loss, and exponential loss are introduced. T…
In this paper, a Bayesian inference technique based on Taylor series approximation of the logarithm of the likelihood function is presented. The proposed approximation is devised for the case, where the prior distribution belongs to the exponential family of distributions. The logarithm of the likelihood function is li…
Three-hidden-layer neural networks can approximate Hölder continuous functions uniformly with exponential rate.
The paper extends properties of smooth functions to closed sets and maps.
The paper extends mixability theory to function-valued forecasts, proving various loss functions are mixable.
We introduce, for every -graded manifold, a formal exponential map defined in a purely algebraic way and study its properties. As an application, we give a simple new construction of a Fedosov type resolution of the algebra of smooth functions of -graded manifolds and we extend the Emmrich--Wein…
New energy functional and fields for Yang-Mills theory, proving monotonicity and vanishing theorems.
Extends likelihood ratio exponential families to analyze various optimization methods.
Extends Stein's lemma to exponential-family mixtures for gradient computation.
Develops a semi-supervised learning method using exponential tilt mixture models.
Paper introduces kernel deformed exponential families for sparse continuous attention.
Extend classical theory of affine processes to path-dependent setting
Analytic networks with bounded coefficients can't outperform polynomial approximations.
Extends online learning to metric spaces using exponential weights.
We study the Dehn function of connected Lie groups. We show that this function is always exponential or polynomially bounded, according to the geometry of weights and of the 2-cohomology of their Lie algebras. Our work, which also addresses algebraic groups over local fields, uses and extends Abels' theory of multiamal…
We obtain a decomposition of the call option price for a very general stochastic volatility diffusion model extending the decomposition obtained by E. Alòs in [2] for the Heston model. We realize that a new term arises when the stock price does not follow an exponential model. The techniques used are non anticipative. …
Extended logarithm for solvable elements in mapping class groups.
We report the proof that the expression of extended Gibrat's law is unique and the probability distribution function (pdf) is also uniquely derived from the law of detailed balance and the extended Gibrat's law. In the proof, two approximations are employed that the pdf of growth rate is described as tent-shaped expone…
New study shows exponential sample growth for ReQU neural networks.
Dropout improves regularization in flexible models for rare features.
The article extends previous work on contracting convex hypersurfaces by nonhomogeneous curvature functions.
We consider the problem of valuing a European option written on an asset whose dynamics are described by an exponential Lévy-type model. In our framework, both the volatility and jump-intensity are allowed to vary stochastically in time through common driving factors -- one fast-varying and one slow-varying. Using Four…
Exponential Lévy processes have been used for modelling financial derivatives because of their ability to exhibit many empirical features of markets. Using their multidimensional analogue, a general analytic pricing formula is obtained, allowing for the direct valuation of multi-asset options on $n \in \z^+$ risky asse…
The abstract theorem extends a Lie group result to Lie groupoids.
We study the geodesic X-ray transform on Cartan-Hadamard manifolds, and prove solenoidal injectivity of this transform acting on functions and tensor fields of any order. The functions are assumed to be exponentially decaying if the sectional curvature is bounded, and polynomially decaying if the sectional curvature de…
Motivated by the pricing of lookback options in exponential Lévy models, we study the difference between the continuous and discrete supremum of Lévy processes. In particular, we extend the results of Broadie et al. (1999) to jump-diffusion models. We also derive bounds for general exponential Lévy models.
TensorPlan shows an exponential lower bound for planning in MDPs with linearly realizable value functions.
New bounds on learning algorithm generalization error derived using information density.
Expressive efficiency refers to the relation between two architectures A and B, whereby any function realized by B could be replicated by A, but there exists functions realized by A, which cannot be replicated by B unless its size grows significantly larger. For example, it is known that deep networks are exponentially…
Method extends eigenfunction construction to non-symmetric spaces.
In this paper, we present a simple analysis of {\bf fast rates} with {\it high probability} of {\bf empirical minimization} for {\it stochastic composite optimization} over a finite-dimensional bounded convex set with exponential concave loss functions and an arbitrary convex regularization. To the best of our knowledg…
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…
A random walk on a separable, geodesic hyperbolic metric space converges to the boundary with probability one when the step distribution supports two independent loxodromics. In particular, the random walk makes positive linear progress. Progress is known to be linear with exponential decay when …
Study the exponential map on surfaces using fluid dynamics.
The paper analyzes optimal dividend and capital injection strategies under time-inconsistent preferences.
Equivalence of convex optimization, saddle-point problems, and variational inequalities is a well-established concept. The variational inequality (VI) is a static problem which is studied under dynamical settings using a framework called the projected dynamical system, whose stationary points coincide with the static s…
The Langevin Algorithm's stationary distribution is shown to be sub-exponential or sub-Gaussian under certain conditions.
Extends DAMs to Gaussian distributions for efficient pattern storage and retrieval.
The paper extends a prediction method to curved spaces.
This paper extends exponential smoothing to distributional time series using Wasserstein distance.
Proposes a new loss function for robust learning.
Large over-parametrized models learned via stochastic gradient descent (SGD) methods have become a key element in modern machine learning. Although SGD methods are very effective in practice, most theoretical analyses of SGD suggest slower convergence than what is empirically observed. In our recent work [8] we analyze…
Study shows exponential convergence in classification errors using random features and SGD.
In this short paper, we overview and extend the results of our papers cond-mat/0001432, cond-mat/0008305, and cond-mat/0103544, where we use an analogy with statistical physics to describe probability distributions of money, income, and wealth in society. By making a detailed quantitative comparison with the available …