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.
Mathematical approach defines stability conditions for ML models.
This paper studies dynamic stochastic optimization problems parametrized by a random variable. Such problems arise in many applications in operations research and mathematical finance. We give sufficient conditions for the existence of solutions and the absence of a duality gap. Our proof uses extended dynamic programm…
This paper provides mathematical foundations for regression methods used in forward initial margin approximation.
New methods solve complex PDEs with mixed boundary conditions.
Physicists explain a mathematical theorem about topological insulators.
The paper synthesizes the mathematics of modeling the future.
The paper proves geometric properties of square tables and saddle surfaces.
Mathematical conditions and practical computations for adversarial robustness measures are established.
This study optimizes crypto-market trading conditions without assuming convexity.
The paper explores risk-minimization for exponential additive models, providing mathematical expressions and numerical examples.
Mathematical analysis improves SGMs, resolving memorization issues.
Mathematical models with time dependent parameters are of great interest in financial Mathematics because they capture real life scenarios in the financial market. In this study, via the Lie group technique, we analyse evolution-type equations with time dependent parameters and give the general symmetry structure of th…
Paper examines two methods for FX market volatility modeling.
Paper proposes a math-inspired L2O model for better generalization.
MFGs explain and enhance generative models, revealing new model types.
The challenge to fruitfully merge state-of-the-art techniques from mathematical finance and numerical analysis has inspired researchers to develop fast deterministic option pricing methods. As a result, highly efficient algorithms to compute option prices in Lévy models by solving partial integro differential equations…
This paper provides a PAC-Bayesian bound for CVaR in machine learning.
The braneworld theory appear with the purpose of solving the problem of the hierarchy of the fundamental interactions. The perspectives of the theory emerge as a new physics, for example, deviation of the law of Newton's gravity. One of the principles of the theory is to suppose that the braneworld is local submanifold…
New method estimates portfolio turnover using covariance matrix of returns.
Study deep neural nets for solving complex insurance equations.
We axiomatically introduce risk-consistent conditional systemic risk measures defined on multidimensional risks. This class consists of those conditional systemic risk measures which can be decomposed into a state-wise conditional aggregation and a univariate conditional risk measure. Our studies extend known results f…
The main purpose of this paper is to formalize the modelling process, analysis and mathematical definition of corruption when entering into a contract between principal agent and producers. The formulation of the problem and the definition of concepts for the general case are considered. For definiteness, all calculati…
We study for which polynomials a thin shell wormhole with a continuous metric (connecting two Schwarzschild spacetimes of the same mass) satisfy the null energy condition (NEC) in -gravity. We avoid junction conditions by using the mathematical framework of the Colombeau algebra which describes a generalized …
New mathematical foundations for stable RKHSs improve system identification.
In a discrete time and multiple-priors setting, we propose a new characterisation of the condition of quasi-sure no-arbitrage which has become a standard assumption. This characterisation shows that it is indeed a well-chosen condition being equivalent to several previously used alternative notions of no-arbitrage and …
We show that near-horizon geometries in the presence of a positive cosmological constant cannot exist with ring topology. In particular, de Sitter black rings with vanishing surface gravity do not exist. Our result relies on a known mathematical theorem which is a straightforward consequence of a type of energy conditi…
The study examines how model predictions hold up under model extensions.
Euler derived elastica equation using modern mathematical concepts.
Conditional mean embeddings (CMEs) have proven themselves to be a powerful tool in many machine learning applications. They allow the efficient conditioning of probability distributions within the corresponding reproducing kernel Hilbert spaces (RKHSs) by providing a linear-algebraic relation for the kernel mean embedd…
Study shows TAR model captures leverage effect in financial series.
It is often stated in papers tackling the task of inferring Bayesian network structures from data that there are these two distinct approaches: (i) Apply conditional independence tests when testing for the presence or otherwise of edges; (ii) Search the model space using a scoring metric. Here I argue that for complete…
Novel approach for creating interpretable classifiers using bilevel optimization of split-rules in NLDTs.
Paper establishes robust no-arbitrage conditions under projective determinacy.
This work proposes a mathematical framework for loss landscapes and optimization in deep neural networks.
We apply Geometric Arbitrage Theory to obtain results in Mathematical Finance, which do not need stochastic differential geometry in their formulation. First, for a generic market dynamics given by a multidimensional Itô's process we specify and prove the equivalence between (NFLVR) and expected utility maximization. A…
Wavelet SGM accelerates generative modeling with linear time complexity.
The goal of this note is to illustrate the impact of a self-financing condition recently introduced by the authors. We present the analyses of two specific applications usually considered in more traditional models in financial mathematics. They include hedging European options with limit orders and the optimal behavio…
We solve the problem of optimal stopping of a Brownian motion subject to the constraint that the stopping time's distribution is a given measure consisting of finitely-many atoms. In particular, we show that this problem can be converted to a finite sequence of state-constrained optimal control problems with additional…
Advanced mathematical relativity course for math and physics students.
Paper proposes ExsdHawkes to model LOBs, capturing volatility dynamics.
A longstanding question in superstring/ theory is does it predict supersymmetry below the string scale? We formulate and discuss a necessary condition for this to be true; this is the mathematical conjecture that all stable, compact Ricci flat manifolds have special holonomy in dimensions below eleven. Almost equiva…
This work concerns the definition and analysis of a new class of Lie systems on Poisson manifolds enjoying rich geometric features: the Lie--Hamilton systems. We devise methods to study their superposition rules, time independent constants of motion and Lie symmetries, linearisability conditions, etc. Our results are i…
The paper surveys mathematical results on filtration enlargement with financial examples.
Mathematical general relativity reviewed.
The paper tackles singularities in diffusion models on submanifolds.
In this paper we outline methodology to efficiently simulate (jump) diffusion bridge sample paths without discretisation error. We achieve this by considering the simulation of conditioned (jump) diffusion bridge sample paths in light of recent work developing a mathematical framework for simulating finite dimensional …
We define two non-linear operations with random (not necessarily closed) sets in Banach space: the conditional core and the conditional convex hull. While the first is sublinear, the second one is superlinear (in the reverse set inclusion ordering). Furthermore, we introduce the generalised conditional expectation of r…
The study finds a lower bound for the diameter of gradient ρ-Einstein solitons.