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 construct explicit solutions to continuous motion of discrete plane curves described by a semi-discrete potential modified KdV equation. Explicit formulas in terms the function are presented. Bäcklund transformations of the discrete curves are also discussed. We finally consider the continuous limit of discrete …
We consider -dimensional discrete motions such that any two neighbouring positions correspond in a pure rotation ("rotating motions"). In the Study quadric model of Euclidean displacements these motions correspond to quadrilateral nets with edges contained in the Study quadric ("rotation nets"). The main focus of ou…
We construct explicit solutions to the discrete motion of discrete plane curves that has been introduced by one of the authors recently. Explicit formulas in terms the function are presented. Transformation theory of the motions of both smooth and discrete curves is developed simultaneously.
New method solves discrete mKdV equation from curve motions.
New geometric transformations link discrete and continuous curve motions.
The discrete sum of geometric Brownian motions plays an important role in modeling stochastic annuities in insurance. It also plays a pivotal role in the pricing of Asian options in mathematical finance. In this paper, we study the probability distributions of the infinite sum of geometric Brownian motions, the sum of …
Study on Brownian motion on discrete curve spaces, proving stochastic completeness.
We study the motion of discrete interfaces driven by ferromagnetic interactions in a two-dimensional periodic environment by coupling the minimizing movements approach by Almgren, Taylor and Wang and a discrete-to-continuous analysis. The case of a homogeneous environment has been recently treated by Braides, Gelli and…
We study the motion of discrete interfaces driven by ferromagnetic interactions on the two-dimensional triangular lattice by coupling the Almgren, Taylor and Wang minimizing movements approach and a discrete-to-continuum analysis, as introduced by Braides, Gelli and Novaga in the pioneering case of the square lattice. …
We study the motion of discrete interfaces driven by ferromagnetic interactions in a two-dimensional low-contrast periodic environment, by coupling the minimizing movements approach by Almgren, Taylor and Wang and a discrete-to-continuum analysis. As in a recent paper by Braides and Scilla dealing with high-contrast pe…
We study the geometry of the inextensible string (the whip) and its discrete approximation (the chain). In the absence of gravity, both motions represent geodesic motions on certain manifolds. We show how the motion of the chain converges to that of a whip, and how the curvature of the chain's configuration space conve…
Derives EoM for DNNs to describe GD dynamics precisely.
The time average of geometric Brownian motion plays a crucial role in the pricing of Asian options in mathematical finance. In this paper we consider the asymptotics of the discrete-time average of a geometric Brownian motion sampled on uniformly spaced times in the limit of a very large number of averaging time steps.…
A linkage mechanism consists of rigid bodies assembled by joints which can be used to translate and transfer motion from one form in one place to another. In this paper, we are particularly interested in a family of spacial linkage mechanisms which consist of -copies of a rigid body joined together by hinges to form…
Lyons and Sullivan have shown how to discretize harmonic functions on a Riemannian manifold whose Brownian motion satisfies a certain recurrence property called -recurrence. We study analogues of this discretization for tensor fields which are harmonic in the sense of the covariant Laplacian. We show that, un…
Deep network predicts action sequences for complex tasks from a scene image.
Study evaluates discretized arbitrage strategies in fractional financial markets.
We study polygonal analogues of several moving boundary problems and their time discretization which preserves the constant area speed property. We establish various polygonal analogues of geometric formulas for moving boundaries and make use of the geometric formulas for our numerical scheme and its analysis of genera…
This work improves motion planning for quadcopters by learning and reasoning about controller performance.
This work compresses sequences by treating them as continuous-time processes, enabling efficient discretization.
In this paper, we present a discrete-type approximation scheme to solve continuous-time optimal stopping problems based on fully non-Markovian continuous processes adapted to the Brownian motion filtration. The approximations satisfy suitable variational inequalities which allow us to construct -optimal stopping tim…
General area-preserving motion of polygonal curves is formulated as a system of ODEs. Solution polygonal curves belong to a prescribed polygonal class, which is similar to the admissible class used in the crystalline curvature flow. The ODEs are discretized implicitly in time keeping a given constant area speed while s…
Deep learning predicts path-dependent processes from historical data.
Global approximation for piecewise linear paths via signatures.
Online review communities are dynamic as users join and leave, adopt new vocabulary, and adapt to evolving trends. Recent work has shown that recommender systems benefit from explicit consideration of user experience. However, prior work assumes a fixed number of discrete experience levels, whereas in reality users gai…
Study on error rates for approximating rough volatility models.
Connections on principal bundles play a fundamental role in expressing the equations of motion for mechanical systems with symmetry in an intrinsic fashion. A discrete theory of connections on principal bundles is constructed by introducing the discrete analogue of the Atiyah sequence, with a connection corresponding t…
We develop variational integrators from discrete Hamiltonian systems with external forces.
Estimates roughness of volatility from discrete variance data.
Bäcklund transformations for smooth and ``space discrete'' Hashimoto surfaces are discussed and a geometric interpretation is given. It is shown that the complex curvature of a discrete space curve evolves with the discrete nonlinear Schrödinger equation (NLSE) of Ablowitz and Ladik, when the curve evolves with the Has…
Continuous time models in the theory of real options give explicit formulas for optimal exercise strategies when options are simple and the price of an underlying asset follows a geometric Brownian motion. This paper suggests a general, computationally simple approach to real options in discrete time. Explicit formulas…
New formulas forecast fractional Brownian motion for financial trading.
New methods solve complex financial equations.
The paper introduces discrete Dirac structures for mechanics, simplifying dynamics.
Paper extends a method to estimate Hurst parameter for rough stochastic volatility models.
Skew parallelogram nets factorize, encompassing discrete differential geometry.
Innovative extensions to option pricing models using asymmetric Brownian motion and random walk approaches.
In a given scenario, simultaneously and accurately predicting every possible interaction of traffic participants is an important capability for autonomous vehicles. The majority of current researches focused on the prediction of an single entity without incorporating the environment information. Although some approache…
Extended Regge complex for linearized Riemann-Cartan geometry and cohomology.
Model rough volatility using RDEs with correlated Brownian motion and fractional Brownian motion.
In this paper, we present a Longstaff-Schwartz-type algorithm for optimal stopping time problems based on the Brownian motion filtration. The algorithm is based on Leão, Ohashi and Russo and, in contrast to previous works, our methodology applies to optimal stopping problems for fully non-Markovian and non-semimartinga…
New perspective on SGD reveals short-range memory effects in deep learning.
A single-vertex origami is a piece of paper with straight-line rays called creases emanating from a fold vertex placed in its interior or on its boundary. The Single-Vertex Origami Flattening problem asks whether it is always possible to reconfigure the creased paper from any configuration compatible with the metric, t…
Optimal strategy for liquidating portfolios under discrete time intervals.
A new framework for pricing the European currency option is developed in the case where the spot exchange rate fellows a time-changed fractional Brownian motion. An analytic formula for pricing European foreign currency option is proposed by a mean self-financing delta-hedging argument in a discrete time setting. The m…
This note clarifies connections between Föllmer process and DDPM sampler.
This paper surveys DRL for autonomous vehicle motion planning.
ES reduces high-probability regret in stochastic linear bandits.