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.
We make posterior sampling in FWI feasible for large surveys.
New method identifies structural parameters without assuming uncorrelated errors.
Paper presents a new insurance model equation for diverse structures.
Proposes MELODIC family for simultaneous binary logistic regression.
Recent work has introduced a simple numerical method for solving partial differential equations (PDEs) with deep neural networks (DNNs). This paper reviews and extends the method while applying it to analyze one of the most fundamental features in numerical PDEs and nonlinear analysis: irregular solutions. First, the S…
Explains fusion for Yang-Baxter equation and braid group.
We establish a new version of the first Noether Theorem, according to which the (equivalence classes of) first integrals of given Euler-Lagrange equations in one independent variable are in exact one-to-one correspondence with the (equivalence classes of) vector fields satisfying two simple geometric conditions, namely…
In some speaker recognition scenarios we find conversations recorded simultaneously over multiple channels. That is the case of the interviews in the NIST SRE dataset. To take advantage of that, we propose a modification of the PLDA model that considers two different inter-session variability terms. The first term is t…
A variational principle is proposed for obtaining the Jacobi equations in systems admitting a Lagrangian description. The variational principle gives simultaneously the Lagrange equations of motion and the Jacobi variational equations for the system. The approach can be of help in finding constants of motion in the Jac…
We give necessary and sufficient local conditions for the simultaneous unitarizability of a set of analytic matrix maps from an analytic 1-manifold into SL_n(C) under conjugation by a single analytic matrix map. We apply this result to the monodromy arising from an integrable partial differential equation to construct …
A model optimizes carbon emission reduction and allowance purchasing for companies.
One popular approach to option pricing in Lévy models is through solving the related partial integro differential equation (PIDE). For the numerical solution of such equations powerful Galerkin methods have been put forward e.g. by Hilber et al. (2013). As in practice large classes of models are maintained simultaneous…
We introduce a method for solving Calderón type inverse problems for semilinear equations with power type nonlinearities. The method is based on higher order linearizations, and it allows one to solve inverse problems for certain nonlinear equations in cases where the solution for a corresponding linear equation is not…
SyGlasso models tensor data dependencies using Sylvester equations.
Develops a neural network approach to solve inverse stochastic problems from particle observations.
We study stochastic differential equations (SDEs) whose drift and diffusion coefficients are path-dependent and controlled. We construct a value process on the canonical path space, considered simultaneously under a family of singular measures, rather than the usual family of processes indexed by the controls. This val…
In this paper, we will give a rigorous construction of the exact discrete Lagrangian formulation associated to a continuous Lagrangian problem. Moreover, we work in the setting of Lie groupoids and Lie algebroids which is enough general to simultaneously cover several cases of interest in discrete and continuous descri…
Some intrinsic tools from the formal theory of variational equations are being demonstrated at work in application to one concrete example of the third-order evolution equation of free relativistic top in three-dimensional space-time. The main goal is to introduce a combined approach consisting in the simultaneous util…
Linear stochastic models and discretized kinetic theory are two complementary analytical techniques used for the investigation of complex systems of economic interactions. The former employ Langevin equations, with an emphasis on stock trade; the latter is based on systems of ordinary differential equations and is bett…
Evolution of planar curves under a nonlocal geometric equation is investigated. It models the simultaneous contraction and growth of carbonate particles called ooids in geosciences. Using classical ODE results and a bijective mapping we demonstrate that the steady parameters associated with the physical environment det…
The paper calibrates SPX and VIX options using optimal transport.
We derive the Black-Scholes-Merton dual equation, which has exactly the same form as the Black-Scholes-Merton equation. The novel and general equation works for options with a payoff of homogeneous of degree one, including European, American, Bermudan, Asian, barrier, lookback, etc., and leads to new insights into pric…
With the advent of modern data collection and storage technologies, data-driven approaches have been developed for discovering the governing partial differential equations (PDE) of physical problems. However, in the extant works the model parameters in the equations are either assumed to be known or have a linear depen…
New theorem connects probabilistic permanental point processes to Monge-Ampère equation.
We discuss a recently proposed variational principle for deriving the variational equations associated to any Lagrangian system. The principle gives simultaneously the Lagrange and the variational equations of the system. We define a new Lagrangian in an extended configuration space ---which we call D'Alambert's--- com…
We explore the application of automated reasoning techniques to unknot detection, a classical problem of computational topology. We adopt a two-pronged experimental approach, using a theorem prover to try to establish a positive result (i.e. that a knot is the unknot), whilst simultaneously using a model finder to try …
Deep neural network generates symbolic equations from data.
This paper optimizes trading strategies to minimize risk and maximize profit while accounting for market uncertainty.
Proves regularity for quasilinear elliptic equations in metric spaces.
We propose a numerical method for solving high dimensional fully nonlinear partial differential equations (PDEs). Our algorithm estimates simultaneously by backward time induction the solution and its gradient by multi-layer neural networks, while the Hessian is approximated by automatic differentiation of the gradient…
Solves initial boundary value problem for vacuum Einstein equations and proves geometric uniqueness.
V-SysId identifies keypoints and 3D system from unlabeled videos.
Growth of spinors in 4D and 3D generalized Seiberg-Witten equations.
Proposes a method to estimate SDE noise from a single trajectory.
Study curvature of piecewise metrics using moving frames.
New geometry theory solves dark matter issues.
Develops methods to solve complex and real Hessian equations.
Researchers find solutions to Einstein equations in higher dimensions.
Veronese webs are rich geometric structures with deep relationships to various domains of mathematics. The PDEs which determine the Veronese web are overdetermined if dim >3, but in the case dim =3 they reduce to a special flavor of a non-linear wave equation. The symmetries embedded in the definition of a Veronese web…
Paper solves complex game theory problems with new equations.
In this paper, we introduce local expressions for discrete Mechanics. To apply our results simultaneously to several interesting cases, we derive these local expressions in the framework of Lie groupoids, following the program proposed by Alan Weinstein in [19]. To do this, we will need some results on the geometry of …
We solve integrable systems to describe the motion of Kaleidocycles.
New algorithm optimizes nonlinear SDEs online with convergence guarantees.
We employ the relationship between contact structures and Beltrami fields derived in part I of this series to construct steady nonsingular solutions to the Euler equations on a Riemannian whose flowlines trace out closed curves of all possible knot and link types simultaneously. Using careful contact-topological …
Proposes PI-VAE for solving SDEs with limited measurements.
We derive one unified formula for Ricci curvature tensor on arbitrary warped product manifold by introducing a new notation for the lift vector and the Levi-Civita connection.This formula is helpful to further consider Ricci flow (RF) and hyperbolic geometric flow (HGF) and evolution equations on warped product manifol…
Paper combines QRM and CNN for better stock option price forecasting.
We extend the Deep Galerkin Method (DGM) introduced in Sirignano and Spiliopoulos (2018)} to solve a number of partial differential equations (PDEs) that arise in the context of optimal stochastic control and mean field games. First, we consider PDEs where the function is constrained to be positive and integrate to uni…