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.
Modified BA algorithm computes RD and DR functions efficiently.
Improved root-finding method for smooth functions.
Root-finding methods improve efficiency of conformal prediction sets.
Improved bounds for Black-Scholes volatility lead to faster root-finding.
Improved MLMC method for robust and efficient probability and density estimation.
Algorithm removes leaves to find root in uniform trees.
We consider numerical schemes for root finding of noisy responses through generalizing the Probabilistic Bisection Algorithm (PBA) to the more practical context where the sampling distribution is unknown and location-dependent. As in standard PBA, we rely on a knowledge state for the approximate posterior of the root l…
Develops a method for learning sparse generalized linear models in high-dimensional data.
Develops new algorithms for solving root-finding problems in large-scale settings.
Optimizes AMM markets with a new framework reducing complex optimization to simpler root finding.
New method solves root-finding problems with faster convergence.
Develops efficient method for nonconvex problems using Regula Falsi.
Method estimates noise variance in Gaussian process regression.
Efficient neural networks compute various differential operators cheaply.
MSLs use parallelizable root-finding for efficient ODE and PDE solutions.
Probabilistic Bisection Algorithm performs root finding based on knowledge acquired from noisy oracle responses. We consider the generalized PBA setting (G-PBA) where the statistical distribution of the oracle is unknown and location-dependent, so that model inference and Bayesian knowledge updating must be performed s…
The Apollonius theorem is generalized for m-simplices, with applications in geometry and optimization.
A new line search rule improves support recovery in high-dimensional data.
Smooth flows for physical systems with smooth energies and forces.
A new algorithm reduces the time and space complexity for multinomial logistic bandits.
New method smooths integrands for efficient option pricing.
We develop a conditional sampling scheme for pricing knock-out barrier options under the Linear Transformations (LT) algorithm from Imai and Tan (2006). We compare our new method to an existing conditional Monte Carlo scheme from Glasserman and Staum (2001), and show that a substantial variance reduction is achieved. W…
Study one-dimensional topological theories with linear generating functions.
Newton's method solves variational problems on manifolds.
We simplify SVI volatility smile constraints for three sub-SVIs without numerical methods.
Stochastic convex optimization problems with expectation constraints (SOECs) are encountered in statistics and machine learning, business, and engineering. In data-rich environments, the SOEC objective and constraints contain expectations defined with respect to large datasets. Therefore, efficient algorithms for solvi…
We found a new simple family of Cantor sets whose projections are one-dimensional.
We create precise formulas for VIX option implied volatility.
Study of one-dimensional non-Hausdorff manifolds and their quotient to CW complexes.
We propose a quasi-Monte Carlo algorithm for pricing knock-out and knock-in barrier options under the Heston (1993) stochastic volatility model. This is done by modifying the LT method from Imai and Tan (2006) for the Heston model such that the first uniform variable does not influence the stochastic volatility path an…
A new metric-based principal curve method learns 1D manifolds from spatial data.
Consider a process, stochastic or deterministic, obtained by using a numerical integration scheme, or from Monte-Carlo methods involving an approximation to an integral, or a Newton-Raphson iteration to approximate the root of an equation. We will assume that we can sample from the distribution of the process from time…
We prove that for compact, non-contractible, one dimensional geodesic spaces, a version of the marked length spectrum conjecture holds. For a compact one dimensional geodesic space X, we define a subspace Conv(X). When X is non-contractible, we show that X deformation retracts to Conv(X). If two such spaces X, Y have t…
The probabilistic bisection algorithm (PBA) solves a class of stochastic root-finding problems in one dimension by successively updating a prior belief on the location of the root based on noisy responses to queries at chosen points. The responses indicate the direction of the root from the queried point, and are incor…
Recently, the decentralized optimization problem is attracting growing attention. Most existing methods are deterministic with high per-iteration cost and have a convergence rate quadratically depending on the problem condition number. Besides, the dense communication is necessary to ensure the convergence even if the …
One-dimensional crystals have convex shapes under certain conditions.
Smooth algebra analysis for one-dimensional singular foliations.
This paper proposes a data-driven approach, by means of an Artificial Neural Network (ANN), to value financial options and to calculate implied volatilities with the aim of accelerating the corresponding numerical methods. With ANNs being universal function approximators, this method trains an optimized ANN on a data s…
We classify the harmonic morphisms with one-dimensional fibres (1) from real-analytic conformally-flat Riemannian manifolds of dimension at least four, and (2) between conformally-flat Riemannian manifolds of dimensions at least three.
It is generally understood that a given one-dimensional diffusion may be transformed by Cameron-Martin-Girsanov measure change into another one-dimensional diffusion with the same volatility but a different drift. But to achieve this we have to know that the change-of-measure local martingale that we write down is a tr…
The paper analyzes the performance of constant step-size stochastic approximation algorithms.
Estimates and optimizes UBSR risk in recursive settings.
We obtain a deterministic characterisation of the \emph{no free lunch with vanishing risk}, the \emph{no generalised arbitrage} and the \emph{no relative arbitrage} conditions in the one-dimensional diffusion setting and examine how these notions of no-arbitrage relate to each other.
In this paper we continue our studies of the one dimensional conformal metric flows, which were introduced in [8]. In this part we mainly focus on evolution equations involving fourth order derivatives. The global existence and exponential convergence of metrics for the 1-Q and 4-Q flows are obtained.
We prove that, from an Einstein manifold of dimension greater than or equal to five, there are just two types of harmonic morphism with one-dimensional fibres. This generalizes a result of R.L. Bryant who obtained the same conclusion under the assumption that the domain has constant curvature.
The study examines different types of equilibria for stopping problems in one-dimensional diffusion processes.
Suppose that f and g are Markov surjections, each defined on a wedge of circles, each fixing the branch point and having the branch point as the only critical value. We show that if the points in the inverse limit spaces associated with f and g corresponding to the branch point are distinguished then these inverse limi…
In their study of fundamental groups of one-dimensional path-connected compact metric spaces, Cannon and Conner have asked: Is there a tree-like object that might be considered the topological Cayley graph? We answer this question in the positive and provide a combinatorial description of such an object.