arXiv research

LOV model calibrates European and American options with path-dependent volatility.

We introduce cylindrical projections to simulate infinite-dimensional occupation flows of diffusions.

Develops a new calculus for stochastic processes with occupation flows.

Study how knots occupy space using topological methods.

We present a new proof of the bi-Lipschitz model theorem, which occupies the main part of the Ending Lamination Conjecture proved by Minsky and Brock-Canary-Minsky. Our proof is done by using techniques of standard hyperbolic geometry as much as possible.

In this paper is proposed a kind of model theory for our axiomatic differential geometry. It is claimed that smooth manifolds, which have occupied the center stage in differential geometry, should be replaced by functors on the category of Weil algebras. Our model theory is geometrically natural and conceptually motiva…

We describe society as a nonequilibrium probabilistic system: N individuals occupy W resource states in it and produce entropy S over definite time periods. Resulting thermodynamics is however unusual because a second entropy, H, measures a typically social feature, inequality or diversity in the distribution of availa…

The paper sketches a recent progress and formulates several open problems in studying equivariant quasiconformal and quasisymmetric homeomorphisms in negatively curved spaces as well as geometry and topology of noncompact geometrically finite negatively curved manifolds and their boundaries at infinity having Carnot--C…

ISP improves GNN expressivity by stratifying nodes based on graph invariants.

Gerbes encode spectral gaps in topological insulators.

We extend the topological field theory (``itsy bitsy topological field theory"') of our previous work from mod-2 to twisted coefficients. This topological field theory is derived from sutured Floer homology but described purely in terms of surfaces with signed points on their boundary (occupied surfaces) and curves on …

We introduce general scattering transforms as mathematical models of deep neural networks with l2 pooling. Scattering networks iteratively apply complex valued unitary operators, and the pooling is performed by a complex modulus. An expected scattering defines a contractive representation of a high-dimensional probabil…

We prove the double bubble conjecture in the three-sphere $S^3$ and hyperbolic three-space $H^3$ in the cases where we can apply Hutchings theory: 1) in $S^3$, each enclosed volume and the complement occupy at least 10% of the volume of $S^3$; 2) in $H^3$, the smaller volume is at least 85% that of the larger. A balanc…

This paper provides an attempt to formalize Hayek's notion of spontaneous order within the framework of the Arrow-Debreu economy. Our study shows that if a competitive economy is enough fair and free, then a spontaneous economic order shall emerge in long-run competitive equilibria so that social members together occup…

In this paper, we provide families of second order non-linear partial differential equations, describing pseudospherical surfaces (pss equations), with the property of having local isometric immersions in E^3, with principal curvatures depending on finite-order jets of solutions of the differential equation. These equa…

The paper contains a combinatorial theorem (the sequence of Newton polygons of a reccurent sequence of polynomials is quasi-linear) and two applications of it in classical and quantum topology, namely in the behavior of the $A$-polynomial and a fixed quantum invariant (such as the Jones polynomial) under filling. Our c…

We survey the main ideas in the early history of the subjects on which Riemann worked and that led to some of his most important discoveries. The subjects discussed include the theory of functions of a complex variable, elliptic and Abelian integrals, the hypergeometric series, the zeta function, topology, differential…

Based on the approach of flow distances, the international trade flow system is studied from the perspective of multi-layer flow network. A model of multi-layer flow network is proposed for modelling and analyzing multiple types of flows in flow systems. Then, flow distances are introduced, and symmetric minimum flow d…

In this paper we show that in some cases the E.Hopf rigidity phenomenon admits quantitative interpretation. More precisely we estimate from above the measure of the set $\mathcal{M}$ swept by minimal orbits. These estimates are sharp, i.e. if $\mathcal{M}$ occupies the whole phase space we recover the E.Hopf rigidity. …

In this paper we show that the non-alternating torus knots are homologically thick, i.e. that their Khovanov homology occupies at least three diagonals. Furthermore, we show that we can reduce the number of full twists of the torus knot without changing certain part of its homology, and consequently, we show that there…

In "Width complexes for knots and 3-manifolds," Jennifer Schultens defines the width complex for a knot in order to understand the different positions a knot can occupy in the 3-sphere and the isotopies between these positions. She poses several questions about these width complexes; in particular, she asks whether the…

Embedding representations power machine intelligence in many applications, including recommendation systems, but they are space intensive -- potentially occupying hundreds of gigabytes in large-scale settings. To help manage this outsized memory consumption, we explore mixed dimension embeddings, an embedding layer arc…

MacroHFT uses memory and context-aware reinforcement learning to improve HFT performance.

Model selection is a problem that has occupied machine learning researchers for a long time. Recently, its importance has become evident through applications in deep learning. We propose an agreement-based learning framework that prevents many of the pitfalls associated with model selection. It relies on coupling the t…

An analysis of the Japanese credit market in 2004 between banks and quoted firms is done in this paper using the tools of the networks theory. It can be pointed out that: (i) a backbone of the credit channel emerges, where some links play a crucial role; (ii) big banks privilege long-term contracts; the "minimal spanni…

We extend the results and methods of \cite{MP} to prove the existence of constant positive scalar curvature metrics $g$ which are complete and conformal to the standard metric on $S^N \setminus Λ$, where $Λ$ is a disjoint union of submanifolds of dimensions between 0 and $(N-2)/2$. The existence of solutions with isola…

LNPE enhances local connections in embeddings using extended neighbor propagation.

Exact relationships found between ATM slope, volatility swap, and zero vanna.

Study local volatility from rough volatility models, finding new skew rule.

The paper deals with bonus-malus systems with different claim types and varying deductibles. The premium relativities are softened for the policyholders who are in the malus zone and these policyholders are subject to per claim deductibles depending on their levels in the bonus-malus scale and the types of the reported…

Enhanced volatility forecasting using options data and rough volatility model.

In this work we show that the systems of balance equations (balance systems) of continuum thermodynamics occupy a natural place in the variational bicomplex formalism. We apply the vertical homotopy decomposition to get a local splitting (in a convenient domain) of a general balance system as the sum of a Lagrangian pa…

We consider an asset whose risk-neutral dynamics are described by a general class of local-stochastic volatility models and derive a family of asymptotic expansions for European-style option prices and implied volatilities. Our implied volatility expansions are explicit; they do not require any special functions nor do…

Proposes a new method for efficient manifold denoising robust to high dimensional noise.

Study on estimating volatility of volatility using Fourier methods and provides insights into volatility dynamics.

Extends Heston model with local volatility for better fit to market volatilities.

The paper values perpetual callable American volatility options using a mean-reverting volatility model.

Hierarchical analysis is considered and a multilevel model is presented in order to explore causality, chance and complexity in financial economics. A coupled system of models is used to describe multilevel interactions, consistent with market data: the lowest level is occupied by agents generating the prices of indivi…

The stochastic volatility model is one of volatility models which infer latent volatility of asset returns. The Bayesian inference of the stochastic volatility (SV) model is performed by the hybrid Monte Carlo (HMC) algorithm which is superior to other Markov Chain Monte Carlo methods in sampling volatility variables. …

In this paper, Malliavin calculus is applied to arrive at exact formulas for the difference between the volatility swap strike and the zero vanna implied volatility for volatilities driven by fractional noise. To the best of our knowledge, our estimate is the first to derive the rigorous relationship between the zero v…

Develops a martingale expansion for stochastic volatility models.

Study large deviations in fractional volatility models with non-Gaussian volatility.

Estimates volatility of volatility and leverage effect using high-frequency options data.

This study compares three volatility metrics for Bitcoin, highlighting high expected volatility.

Currency volatility shocks predict lower excess returns, and buying weak transmitters outperforms selling strong ones.

Bayesian nonparametric (BNP) models provide elegant methods for discovering underlying latent features within a data set, but inference in such models can be slow. We exploit the fact that completely random measures, which commonly used models like the Dirichlet process and the beta-Bernoulli process can be expressed a…

We applied Generative Adversarial Networks (GANs) to learn a model of DOOM levels from human-designed content. Initially, we analysed the levels and extracted several topological features. Then, for each level, we extracted a set of images identifying the occupied area, the height map, the walls, and the position of ga…

The article reviews how to set stochastic volatility model parameters.