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.
Unified framework for T-duality in both trivial and non-trivial topologies.
This paper proposes a general duality framework for the problem of minimizing a convex integral functional over a space of stochastic processes adapted to a given filtration. The framework unifies many well-known duality frameworks from operations research and mathematical finance. The unification allows the extension …
Unified framework for exceptional and generalised geometry, and Poisson-Lie duality.
Geometric framework for inverse problems using foliations and dual connections.
Unified proof of four Bavard dualities and new results on quasimorphisms.
We analyze random feature and two-layer neural networks using duality framework.
We develop a general theory of convex duality for certain singular control problems, taking the abstract results by Kramkov and Schachermayer (1999) for optimal expected utility from nonnegative random variables to the level of optimal expected utility from increasing, adapted controls. The main contributions are the f…
We prove a general duality result for multi-stage portfolio optimization problems in markets with proportional transaction costs. The financial market is described by Kabanov's model of foreign exchange markets over a finite probability space and finite-horizon discrete time steps. This framework allows us to compare v…
We investigate pricing-hedging duality for American options in discrete time financial models where some assets are traded dynamically and others, e.g. a family of European options, only statically. In the first part of the paper we consider an abstract setting, which includes the classical case with a fixed reference …
Develops parametrised Poincaré duality for equivariant fixed points.
Solves risk-sensitive investment via duality, entropic regularization, and RL.
The main result of this paper is that, off of a `fundamental class' in degree 1, the linearized Legendrian contact homology obeys a version of Poincare duality between homology groups in degrees k and -k. Not only does the result itself simplify calculations, but its proof also establishes a framework for analyzing coh…
Study binary perceptrons' capacity using random duality theory.
Generative adversarial network (GAN) is a minimax game between a generator mimicking the true model and a discriminator distinguishing the samples produced by the generator from the real training samples. Given an unconstrained discriminator able to approximate any function, this game reduces to finding the generative …
We give a covariant realization of the doubled sigma-model formulation of duality-symmetric string theory within the general framework of para-Hermitian geometry. We define a notion of generalized metric on a para-Hermitian manifold and discuss its relation to Born geometry. We show that a Born geometry uniquely define…
This work studies the strong duality of non-convex matrix factorization problems: we show that under certain dual conditions, these problems and its dual have the same optimum. This has been well understood for convex optimization, but little was known for non-convex problems. We propose a novel analytical framework an…
In this paper we generalize the framework of the feasible descent method (FDM) to a randomized (R-FDM) and a coordinate-wise random feasible descent method (RC-FDM) framework. We show that the famous SDCA algorithm for optimizing the SVM dual problem, or the stochastic coordinate descent method for the LASSO problem, f…
This paper connects geometric diagrams to spherical T-duality.
A new robust Wasserstein distance is proposed to handle outliers in probability distributions.
This is the second in a series of papers intended to set up a framework to study categories of modules in the context of non-commutative geometries. In \cite{mem} we introduced the basic DG category $\Pc_{\A^\bullet}$, the perfect category of $\A^\bullet$, which corresponded to the category of coherent sheaves on a com…
The paper applies Poincaré duality to supergravity, proving its equivalence to other formulations.
This paper introduces a novel monotone curve estimation framework based on convex duality.
Introduces Legendre bundle for dually flat manifolds and quantum field theories.
We consider a financial market where stocks are available for dynamic trading, and European and American options are available for static trading (semi-static trading strategies). We assume that the American options are infinitely divisible, and can only be bought but not sold. In the first part of the paper, we work w…
We study twisted N=2 superconformal gauge theory on a product of two Riemann surfaces Sigma and C. The twisted theory is topological along C and holomorphic along Sigma and does not depend on the gauge coupling or theta-angle. Upon Kaluza-Klein reduction along Sigma, it becomes equivalent to a topological B-model on C …
This note is meant to introduce the reader to a duality principle for nonlinear equations that recently appeared in the literature. Motivations come from the desire to give a unifying potential-theoretic framework for various maximum principles at infinity appearing in the literature (Ekeland, Omori-Yau, Pigola-Rigoli-…
Dirichlet-Neumann duality for Riemannian submersions
This note provides a novel, simple analysis of the method of conjugate gradients for the minimization of convex quadratic functions. In contrast with standard arguments, our proof is entirely self-contained and does not rely on the existence of Chebyshev polynomials. Another advantage of our development is that it clar…
The paper extends collective arbitrage concepts to multi-agent markets with cooperation.
This work applies Double Field Theory to four-dimensional manifolds, revealing connections to integrability and twistor theory.
Defines formal vertex laws related to Lie conformal algebras.
An affine Cartan calculus is developed. The concepts of special affine bundles and special affine duality are introduced. The canonical isomorphisms, fundamental for Lagrangian and Hamiltonian formulations of the dynamics in the affine setting are proved.
Proves Poincaré duality for Hopf algebroids with bijective antipode.
A supervised learning framework has been proposed for the situation where each training data is provided with a complementary label that represents a class to which the pattern does not belong. In the existing literature, complementary-label learning has been studied independently from ordinary-label learning, which as…
Unified framework for DRO using OT with constraints.
New proof of chain duality for simplicial complexes.
Introduces Kähler duality between domains in complex space.
Research on dualities in geometric stereotypes.
We argue that G_2 manifolds for M-theory admitting string theory Calabi-Yau duals are fibered by coassociative submanifolds. Dual theories are constructed using the moduli space of M5-brane fibers as target space. Mirror symmetry and various string and M-theory dualities involving G_2 manifolds may be incorporated into…
Duality restored in gauge theory, gravity, and string theory models.
Verma Howe duality connects tensor products of Verma modules to LKB representations.
Cohomological and homological spectral sequences are shown to be isomorphic.
Unified framework for model- and value-optimistic reinforcement learning.
New method calculates super-hedging prices with transaction costs.
In these lectures we present a general introduction to topological quantum field theories. These theories are discussed in the framework of the Mathai-Quillen formalism and in the context of twisted N=2 supersymmetric theories. We discuss in detail the recent developments in Donaldson-Witten theory obtained from the ap…
Geometric framework for CFMMs simplifies many results.
We analyze deep neural networks using convex duality to reveal hidden layer structures.
Generalizes double transgression formulas on complex manifolds.