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.
The paper explains how curves evolve from one envelope to another using singularity theory.
Study shows bi-Hamiltonian structure for polygon evolutions in centro-affine space.
This paper gives two methods for constructing associative 3-folds in R^7, based around the fundamental idea of evolution equations, and uses these methods to construct examples of these geometric objects. The paper is a generalisation of the work by Joyce in math.DG/0008021, math.DG/0008155, math.DG/0010036 and math.DG…
New AMP algorithm estimates signals and latent variables in mixed regression models.
In this paper we discuss some affine properties of convex equal-area polygons, which are convex polygons such that all triangles formed by three consecutive vertices have the same area. Besides being able to approximate closed convex smooth curves almost uniformly with respect to affine length, convex equal-area polygo…
The paper shows that energy futures yield curves have an affine geometry.
A new statistical model uses Orlicz-Sobolev spaces with Gaussian weight.
This project improves model robustness to affine transformations.
The paper proves an inequality and describes a curve flow in centro-affine geometry.
In this paper we classify convex compact ancient solutions to the affine curve shortening flow: namely, any convex compact ancient solution to the affine curve shortening flow must be a shrinking ellipse. The method combines a rescaling argument inspired by \cite{Wang}, affine invariance of the equation and monotonicit…
The paper studies a specific centro-affine invariant hypersurface flow in R^(n+1).
A common approach to metric-affine, local Poincaré, special-relativistic and Galilei spacetime geometry is developed. Starting from an affine composite bundle, we introduce local reference frames and their evolution along worldlines and we study both, absolute and relative simultaneity postulates, giving rise to altern…
Given a pair of planar curves, one can define its generalized area distance, a concept that generalizes the area distance of a single curve. In this paper, we show that the generalized area distance of a pair of planar curves is an improper indefinite affine spheres with singularities, and, reciprocally, every indefini…
The paper studies extremal hypersurfaces in ellipsoids using centro-affine geometry.
The paper explores fully affine maximal curves and their properties.
A new model captures forward curve dynamics with stochastic volatility.
For a pair of points in a smooth locally convex surface in 3-space, its mid-plane is the plane containing its mid-point and the intersection line of the corresponding pair of tangent planes. In this paper we show that the limit of mid-planes when one point tends to the other along a direction is the Transon plane of th…
We develop a model for the dynamic evolution of default-free and defaultable interest rates in a LIBOR framework. Utilizing the class of affine processes, this model produces positive LIBOR rates and spreads, while the dynamics are analytically tractable under defaultable forward measures. This leads to explicit formul…
Study on the limits of projective special real manifolds and their symmetries.
Study path-dependent affine models under uncertain parameters for financial applications.
The paper studies a heat flow for diffeomorphisms on flat surfaces, preserving their structure.
This paper generalizes the envelope of mid-lines to intermediate lines for a plane curve.
We provide a unified framework for modeling LIBOR rates using general semimartingales as driving processes and generic functional forms to describe the evolution of the dynamics. We derive sufficient conditions for the model to be arbitrage-free which are easily verifiable, and for the LIBOR rates to be true martingale…
This is the third in a series of papers constructing explicit examples of special Lagrangian submanifolds in C^m. The previous paper in the series, math.DG/0008155, defined the idea of evolution data, which includes an (m-1)-submanifold P in R^n, and constructed a family of special Lagrangian m-folds N in C^m, which ar…
We introduce a tractable multi-currency model with stochastic volatility and correlated stochastic interest rates that takes into account the smile in the FX market and the evolution of yield curves. The pricing of vanilla options on FX rates can be performed effciently through the FFT methodology thanks to the affinit…
The paper provides bounds for pricing Guaranteed Annuity Options under stochastic interest and mortality rates.
The CSA-ES is an Evolution Strategy with Cumulative Step size Adaptation, where the step size is adapted measuring the length of a so-called cumulative path. The cumulative path is a combination of the previous steps realized by the algorithm, where the importance of each step decreases with time. This article studies …
We study the relation between the centro-affine geometry of star-shaped planar curves and the projective geometry of parametrized maps into $\RP^1$. We show that projectivization induces a map between differential invariants and a bi-Poisson map between Hamiltonian structures. We also show that a Hamiltonian evolution …
EAP clusters evolving data, promoting temporal smoothness and automatic cluster tracking.
Develops Hamilton-Jacobi theory for non-conservative field theories in k-contact geometry.
Integrable flows on null curves in anti-de Sitter 3-space studied.
Unified theory of -expectations derived from chaotic dynamics.
New model improves European inflation and interest rate predictions.
The paper studies distributions and controllability in quantum mechanical systems.
Study geodesic and affine Killing completeness in homogeneous affine surfaces.
Almost Zoll affine surface found on cylinder.
We study affine maps between affine manifolds. Even when the fibers are compact and diffeomorphic, two of them can inherit different affine structures from the source space. This leads to a fixed linear holonomy deformation theory of the affine structure of an affine manifold. We found various conditions which make the…
Study finds solutions for degenerate affine curve shortening flow.
The paper introduces a new geometric capacity and proves inequalities related to it.
Study affine curvature lines on surfaces in 3D space.
Model captures rough volatility and jump clustering in stock vol dynamics.
The calculus correspondence has been known to exist between generic pedal evolutions and generic wave front evolutions. In this paper, we first extend the known results on the calculus correspondence to evolutions with multi-parameters, and then give applications of calculus correspondence. Moreover, we discuss the pos…
An affine manifold is a manifold with torsion-free flat affine connection. A geometric topologist's definition of an affine manifold is a manifold with an atlas of charts to the affine space with affine transition functions; a radiant affine manifold is an affine manifold with holonomy consisting of affine transformati…
In this paper, we show that a compact affine manifold endowed with an Affine Anosov transformation is finitely covered by a complete affine nilmanifold.
Proofs for decomposing branched affine surfaces into triangles and cylinders.
This thesis is devoted to the study of affine processes and their applications in financial mathematics. In the first part we consider the theory of time-inhomogeneous affine processes on general state spaces. We present a concise setup for time-inhomogeneous Markov processes. For stochastically continuous affine proce…
Affine maps on tori preserve lines.
Study on completeness in affine and statistical geometry.