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.
Paper benchmarks machine learning for detecting process curve drifts.
Yield curve forecasting is an important problem in finance. In this work we explore the use of Gaussian Processes in conjunction with a dynamic modeling strategy, much like the Kalman Filter, to model the yield curve. Gaussian Processes have been successfully applied to model functional data in a variety of application…
A new model for curves on manifolds using rolling operations.
Modeling trading volume curves using hierarchical Poisson processes.
Nelson and Siegel curves are widely used to fit the observed term structure of interest rates in a particular date. By the other hand, several interest rate models have been developed such their initial forward rate curve can be adjusted to any observed data, as the Ho-Lee and the Hull and White one factor models. In t…
The paper explores using machine learning for yield curve calibration in multiple markets.
We develop and apply an approach for analyzing multi-curve data where each curve is driven by a latent state process. The state at any particular point determines a smooth function, forcing the individual curve to switch from one function to another. Thus each curve follows what we call a switching nonparametric regres…
Efficiently models learning curves using Gaussian processes with latent Kronecker structure.
Combines Bézier curves with Gaussian processes for better sequential data modeling.
A new approach for functional data description is proposed in this paper. It consists of a regression model with a discrete hidden logistic process which is adapted for modeling curves with abrupt or smooth regime changes. The model parameters are estimated in a maximum likelihood framework through a dedicated Expectat…
We develop a modelling framework for multiple yield curves driven by continuous-state branching processes with immigration (CBI processes). Exploiting the self-exciting behavior of CBI jump processes, this approach can reproduce the relevant empirical features of spreads between different interbank rates. In particular…
New curve flow preserves area and converges to a circle.
We have introduce a new vision of stochastic processes through the geometry induced by the dilation. The dilation matrices of a given processes are obtained by a composition of rotations matrices, contain the measure information in a condensed way. Particularly interesting is the fact that the obtention of dilation mat…
The general problem of asset pricing when the discount rate differs from the rate at which an asset's cash flows accrue is considered. A pricing kernel framework is used to model an economy that is segmented into distinct markets, each identified by a yield curve having its own market, credit and liquidity risk charact…
Two flows for convex curves converge to circles smoothly.
The paper proposes a new method for modeling and quantifying uncertainty in multiple closed curves.
Predict missing and future data points in light curves using scalable Gaussian Processes.
We present a new mixture model-based discriminant analysis approach for functional data using a specific hidden process regression model. The approach allows for fitting flexible curve-models to each class of complex-shaped curves presenting regime changes. The model parameters are learned by maximizing the observed-da…
It is shown that the tessellation of a compact, negatively curved surface induced by a typical long geodesic segment, when properly scaled, looks locally like a Poisson line process. This implies that the global statistics of the tessellation -- for instance, the fraction of triangles -- approach those of the limiting …
We provide a general and tractable framework under which all multiple yield curve modeling approaches based on affine processes, be it short rate, Libor market, or HJM modeling, can be consolidated. We model a numeraire process and multiplicative spreads between Libor rates and simply compounded OIS rates as functions …
We define and study a discrete process that generalizes the convex-layer decomposition of a planar point set. Our process, which we call "homotopic curve shortening" (HCS), starts with a closed curve (which might self-intersect) in the presence of a set of point obstacles, and evolves in discrete…
The process of un-reduction, a sort of reversal of reduction by the Lie group symmetries of a variational problem, is explored in the setting of field theories. This process is applied to the problem of curve matching in the plane, when the curves depend on more than one independent variable. This situation occurs in a…
A new model captures forward curve dynamics with stochastic volatility.
A meta-learning approach for efficient algorithm selection in budget-limited scenarios.
In this paper, we study the modeling and the classification of functional data presenting regime changes over time. We propose a new model-based functional mixture discriminant analysis approach based on a specific hidden process regression model that governs the regime changes over time. Our approach is particularly a…
The purpose of this paper relies on the study of long term affine yield curves modeling. It is inspired by the Ramsey rule of the economic literature, that links discount rate and marginal utility of aggregate optimal consumption. For such a long maturity modelization, the possibility of adjusting preferences to new ec…
The paper examines the behavior of Weierstrass measures on stable curves as they approach a nodal stable curve.
Study on stochastic covariant derivatives in curved space-time.
Study on curve shortening flow in 3D space curves, showing convexity preservation and avoidance principle.
Study active nematic forces on curved surfaces, revealing new coupling mechanisms.
Derives conformal parameters of curves using inscribed circular polygons.
The recent financial crisis has led to so-called multi-curve models for the term structure. Here we study a multi-curve extension of short rate models where, in addition to the short rate itself, we introduce short rate spreads. In particular, we consider a Gaussian factor model where the short rate and the spreads are…
In this paper we develop a framework for discretely compounding interest rates which is based on the forward price process approach. This approach has a number of advantages, in particular in the current market environment. Compared to the classical as well as the Lévy Libor market model, it allows in a natural way for…
Physics-constrained GP predicts material states under shockwave conditions.
Bayesian nonparametric method partitions shapes using curves.
We complete the remaining cases of the conjecture predicting existence of infinitely many rational curves on K3 surfaces in characteristic zero, prove almost all cases in positive characteristic and improve the proofs of the previously known cases. To achieve this, we introduce two new techniques in the deformation the…
This paper is devoted to the complete classification of space curves under affine transformations in the view of Cartan's theorem. Spivak has introduced the method but has not found the invariants. Furthermore, for the first time, we propound a necessary and sufficient condition for the invariants. Then, we study the s…
We introduce a new deep-learning based algorithm to evaluate options in affine rough stochastic volatility models. Viewing the pricing function as the solution to a curve-dependent PDE (CPDE), depending on forward curves rather than the whole path of the process, for which we develop a numerical scheme based on deep le…
The paper proves an inequality and describes a curve flow in centro-affine geometry.
The goal of this note is to prove a compact embedding result for spaces of forward rate curves. As a consequence of this result, we show that any forward rate evolution can be approximated by a sequence of finite dimensional processes in the larger state space.
Any two equivalent discrete curves must have the same invariants at the corresponding points under an affine transformation. In this paper, we construct the moving frame and invariants for the discrete centroaffine curves, which could be used to discriminate the same discrete curves from different graphics, and estimat…
Statistical approaches for Functional Data Analysis concern the paradigm for which the individuals are functions or curves rather than finite dimensional vectors. In this paper, we particularly focus on the modeling and the classification of functional data which are temporal curves presenting regime changes over time.…
The paper studies multi-curve interest rate models and their consistency and finite-dimensional realizations.
In this paper we provide a classification of fundamental group elements representing simple closed curves on the punctured Klein bottle, Similar to the Birman-Series classification of curves on the punctured torus[1]. In the process, an explicit description of the mapping class group is given. We then apply this to giv…
The article presents a new non-parametric approach for forecasting mortality and fertility using Gaussian process regression.
For a polygon in Euclidean space we consider a transformation T which is obtained by applying the midpoints polygon construction twice and using an index shift. For a closed polygon this is a curve shortening process. A polygon is called (affine) soliton of the transformation T if its image under T is an affine image o…
In her seminal 2008 paper, Maryam Mirzakhani showed that the ratio that two topological types of curves occur in is a rational number. In this paper we describe the process by which we obtained experimental evidence that separating and non-separating curves on the surface of genus two occur in the ratio 1 : 48.
We consider learning on graphs, guided by kernels that encode similarity between vertices. Our focus is on random walk kernels, the analogues of squared exponential kernels in Euclidean spaces. We show that on large, locally treelike, graphs these have some counter-intuitive properties, specifically in the limit of lar…