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.
Study Galois groupoids of discret Painlevé equations.
We prove that the N-colored Jones polynomial for the torus knot T_{s,t} satisfies the second order difference equation, which reduces to the first order difference equation for a case of T_{2,2m+1}. We show that the A-polynomial of the torus knot can be derived from this difference equation. Also constructed is a q-hyp…
This work extends set-valued risk measures to discrete time, using difference inclusions and equations.
Paper constructs braid invariants using tropical Ptolemy equation.
Introduces modular -holonomic modules to solve -difference equations.
Ghost points affect stability in finite difference schemes for diffusion equations.
In this paper we develop an asymptotic analysis for formal and actual solutions of q-difference equations, under a regularity assumption. In particular, evaluations of regular solutions of regular q-difference equations have an exponential growth rate which can be computed from the q-difference equation. The motivation…
We study the space of linear difference equations with periodic coefficients and (anti)periodic solutions. We show that this space is isomorphic to the space of tame frieze patterns and closely related to the moduli space of configurations of points in the projective space. We define the notion of combinatorial Gale tr…
Study of 2d gauged linear sigma models to derive difference equations and spectral data.
Miura-type transformations (MTs) are an essential tool in the theory of integrable nonlinear partial differential and difference equations. We present a geometric method to construct MTs for differential-difference (lattice) equations from Darboux-Lax representations (DLRs) of such equations. The method is applicable t…
Study non-perturbative quantum geometry of string theories using finite difference equations and resurgence analysis.
A notion of implicit difference equation on a Lie groupoid is introduced and an algorithm for extracting the integrable part (backward or/and forward) is formulated. As an application, we prove that discrete Lagrangian dynamics on a Lie groupoid may be described in terms of Lagrangian implicit difference equations …
In this paper we introduce a new equation on the compact Kahler manifolds. Solution of this equation corresponds to the Calabi-Yau metric. New equation differs from the Monge--Ampere equation considered by Calabi and Yau.
Study BSΔE on lattices for asset price analysis.
Novel approach ensures stability of compact schemes for variable PDEs.
A variational inequality for pricing the perpetual American option and the corresponding difference equation are considered. First, the maximum principle and uniqueness of the solution to variational inequality for pricing the perpetual American option are proved. Then the maximum principle, the existence and uniquenes…
Simpler equations derived for knot polynomials coefficients, forming a ring.
New gradient estimates for heat equation on Riemannian manifolds.
FDNet learns PDEs from data with fast predictions.
A new option pricing model handles non-constant risk aversion and transaction costs.
The paper proposes a different method of solving a simplified version of the Black-Scholes equation. This paper will discuss the importance of the Black-Scholes equation and its applications in finance.
This is an exposition of results on the existence problem of -injective immersed and embedded surfaces in graph-manifolds, and also of nonpositively curved metrics on graph-manifolds, obtained by different authors. The results are represented from a unified point of view based on the notion of compatible cohomolog…
We come up with infinite-dimensional prequantum line bundles and moment map interpretations of three different sets of equations - the generalised Monge-Amp`ere equation, the almost Hitchin system, and the Calabi-Yang-Mills equations. These are all perturbations of already existing equations. Our construction for the g…
What is the suitable Laplace operator on vector fields for the Navier-Stokes equation on a Riemannian manifold? In this note, by considering Nash embedding, we will try to elucidate different aspects of different Laplace operators such as de Rham-Hodge Laplacian as well as Ebin-Marsden's Laplacian. A probabilistic repr…
Paper compares five surface Navier-Stokes derivations and finds some are equivalent.
Approximate symmetries of geodesic equations on 2-spheres are studied. These are the symmetries of the perturbed geodesic equations which represent approximate path of a particle rather than exact path. After giving the exact symmetries of the geodesic equations, two different approaches to study the approximate symmet…
Study on how soliton equations form singularities using L,A,B-triples.
We explore the geometry of the Nahm-Schmid equations, a version of Nahm's equations in split signature. Our discussion ties up different aspects of their integrable nature: dimensional reduction from the Yang--Mills anti-self-duality equations, explicit solutions, Lax-pair formulation, conservation laws and spectral cu…
Study Berry connections for 2d GLSMs, linking to cohomology theories.
Unified framework for implicit generative models with theoretical guarantees.
Long and short memory in economic processes is usually described by the so-called discrete fractional differencing and fractional integration. We prove that the discrete fractional differencing and integration are the Grunwald-Letnikov fractional differences of non-integer order d. Equations of ARIMA(p,d,q) and ARFIMA(…
Quantum K-theory of quintic 3-fold conjectured with non-polynomial coefficients.
We derive a priori estimates for solutions of a general class of fully non-linear equations on compact Hermitian manifolds. Our method is based on ideas that have been used for different specific equations, such as the complex Monge-Ampère, Hessian and inverse Hessian equations. As an application we solve a class of He…
The Seiberg-Witten equations are defined on certain complex line bundles over smooth oriented four manifolds. When the base manifold is a complex Kahler surface, the Seiberg-Witten equations are essentially the Abelian vortex equations. Using known non-abelian generalizations of the vortex equations as a guide, we expl…
We establish a general theorem improving regularity of solutions of elliptic pseudodifferential equations. It allows to resolve in a unified way the regularity issue for a broad class of nonlinear elliptic equations and systems appearing in different areas of geometry and analysis.
We construct a three-point compact finite difference scheme on a non-uniform mesh for the time-fractional Black-Scholes equation. We show that for special graded meshes used in finance, the Tavella-Randall and the quadratic meshes the numerical solution has a fourth-order accuracy in space. Numerical experiments are di…
Develops ML method for solving financial equations.
Quantum dilogarithm function proven from a linear difference equation.
This paper proposes an unsupervised learning method to solve heat equations on chips.
DeepONet learns operators for PDEs with varying parameters and initial conditions.
The paper explores variational principles for equations of maximal symmetry, providing new insights and results.
We prove several differential Harnack inequalities for positive solutions to nonlinear backward heat equations with different potentials coupled with the Ricci flow. We also derive an interpolated Harnack inequality for the nonlinear heat equation under the -Ricci flow on a closed surface. These new Harnac…
We study a class of fourth order geometric equations defined on a 4-dimensional compact Riemannian manifold which includes the Q-curvature equation. We obtain sharp estimates on the difference near the blow-up points between a bubbling sequence of solutions and the standard bubble.
Stochastic differential equation approximation for linear TD(0) under Markovian noise
In this note, we derive a Liouville theorem for the complex Monge-Ampère equation. Our result states that if the global solution of the complex Monge-Ampère equation with constant right-hand side differs from a quadratic polynomial solution by $o(\abs{x}^2)$ at infinity, then is a quadratic polynomial.
Investigates differences in solving mean curvature problems in Euclidean and Lorentz-Minkowski spaces.
FiniteNet uses a neural network to improve PDE solving methods.
Finite energy solutions of 4-harmonic and ES-4-harmonic maps are trivial.