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.
Efficiently finds sparse solutions to max-plus equations for convex regression.
This study presents a method for constructing a sequence of approximate solutions of increasing accuracy to general equilibrium models on nonlocal domains. The method is based on a technique originated from dynamical systems theory. The approximate solutions are constructed employing the Contraction Mapping Theorem and…
We study sparse approximate solutions to convex optimization problems. It is known that in many engineering applications researchers are interested in an approximate solution of an optimization problem as a linear combination of elements from a given system of elements. There is an increasing interest in building such …
For optimization on large-scale data, exactly calculating its solution may be computationally difficulty because of the large size of the data. In this paper we consider subsampled optimization for fast approximating the exact solution. In this approach, one gets a surrogate dataset by sampling from the full data, and …
Paper approximates solutions for complex decision processes with limited precision.
Extends rough Heston model solution to general λ.
Develops weak PINNs for efficient manifold solutions of hyperbolic equations.
The paper shows how neural networks can approximate PDEs with polynomial scaling in dimension.
We describe a glueing construction for the Yang-Mills equations in dimension . Our method is based on a construction of approximate solutions, and a detailed analysis of the linearized operator near an approximate solution.
New neural network approach solves Poisson equations efficiently.
Simple DP algorithms find approximate solutions for nonconvex ERM.
In an ordinary feature selection procedure, a set of important features is obtained by solving an optimization problem such as the Lasso regression problem, and we expect that the obtained features explain the data well. In this study, instead of the single optimal solution, we consider finding a set of diverse yet nea…
Deep learning approximates SPDE solutions from noise trajectories.
Paper presents a randomized algorithm for SPCA with high probability approximation.
We develop an efficient method to calibrate CDS spreads using asymptotic approximations.
Finite-gap solutions approximate jets of initial data for certain BKM systems.
In this paper, we apply the method of approximate transformation groups proposed by Baikov, Gaziziv and Ibragimov, to compute the first-order approximate symmetry for the Gardner equations with the small parameters. We compute the optimal system and analyze some invariant solutions of These types of equations. Particul…
We find approximate solutions of partial integro-differential equations, which arise in financial models when defaultable assets are described by general scalar Lévy-type stochastic processes. We derive rigorous error bounds for the approximate solutions. We also provide numerical examples illustrating the usefulness a…
We derive upper bounds on the complexity of ReLU neural networks approximating the solution maps of parametric partial differential equations. In particular, without any knowledge of its concrete shape, we use the inherent low-dimensionality of the solution manifold to obtain approximation rates which are significantly…
The paper studies obstructions to solutions of the Wess-Zumino-Witten equation and its generalizations.
We consider Lipschitz-type backward stochastic differential equations (BSDEs) driven by cylindrical martingales on the space of continuous functions. We show the existence and uniqueness of the solution of such infinite-dimensional BSDEs and prove that the sequence of solutions of corresponding finite-dimensional BSDEs…
This paper proposes an incremental solution to Fast Subclass Discriminant Analysis (fastSDA). We present an exact and an approximate linear solution, along with an approximate kernelized variant. Extensive experiments on eight image datasets with different incremental batch sizes show the superiority of the proposed ap…
Study proves convergence of interest rate model approximations.
Discrete approximation solves Björling's minimal surface problem.
We present a method for obtaining approximate solutions to the problem of optimal execution, based on a signature method. The framework is general, only requiring that the price process is a geometric rough path and the price impact function is a continuous function of the trading speed. Following an approximation of t…
This paper is a follow up to the previous author's paper on convex optimization. In that paper we began the process of adjusting greedy-type algorithms from nonlinear approximation for finding sparse solutions of convex optimization problems. We modified there three the most popular in nonlinear approximation in Banach…
Paper quantifies neural operators' efficiency for solving nonlinear parabolic PDEs.
New algorithm for weighted low rank approximation with provable guarantees.
We develop several deep learning algorithms for approximating families of parametric PDE solutions. The proposed algorithms approximate solutions together with their gradients, which in the context of mathematical finance means that the derivative prices and hedging strategies are computed simulatenously. Having approx…
We study the evolution of hypersurfaces in spacetime initial data sets by their null mean curvature. A theory of weak solutions is developed using the level-set approach. Starting from an arbitrary mean convex, outer untapped hypersurface , we show that there exists a weak solution to the null mean curvatu…
ACOWA improves distributed sparse classification with extra communication round.
Approximates discounted moments for financial products using polynomial expansions.
Neural networks solve SPDEs using Wiener chaos expansion.
Recently, artificial neural networks (ANNs) in conjunction with stochastic gradient descent optimization methods have been employed to approximately compute solutions of possibly rather high-dimensional partial differential equations (PDEs). Very recently, there have also been a number of rigorous mathematical results …
We introduce a general constructive setting of the density ratio estimation problem as a solution of a (multidimensional) integral equation. In this equation, not only its right hand side is known approximately, but also the integral operator is defined approximately. We show that this ill-posed problem has a rigorous …
Deep neural nets approximate high-dimensional HJB equations efficiently.
This paper considers binomial approximation of continuous time stochastic processes. It is shown that, under some mild integrability conditions, a process can be approximated in mean square sense and in other strong metrics by binomial processes, i.e., by processes with fixed size binary increments at sampling points. …
In this work, we provide theoretical guarantees for reward decomposition in deterministic MDPs. Reward decomposition is a special case of Hierarchical Reinforcement Learning, that allows one to learn many policies in parallel and combine them into a composite solution. Our approach builds on mapping this problem into a…
We study randomized sketching methods for approximately solving least-squares problem with a general convex constraint. The quality of a least-squares approximation can be assessed in different ways: either in terms of the value of the quadratic objective function (cost approximation), or in terms of some distance meas…
We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the efficient frontier of optimal objective value versus risk of constraint violation. …
Paper offers a simpler solution for managing complex financial options.
This work tackles Bayesian neural networks by addressing loss landscape symmetries.
We study positive solutions of the Yamabe equation with isolated singularity and prove the existence of solutions with prescribed asymptotic expansions near singular points and an arbitrarily high order of approximation.
We present a framework for recovering/approximating unknown time-dependent partial differential equation (PDE) using its solution data. Instead of identifying the terms in the underlying PDE, we seek to approximate the evolution operator of the underlying PDE numerically. The evolution operator of the PDE, defined in i…
Dynamic submodular maximization with consistency constraints.
Study on non-negative solutions for stochastic Volterra equations with jumps.
New method approximates Gaussian curvature on discrete surfaces.
Paper interprets ResNets via gate-network controls and deep-layer classifications.