arXiv research

Optimal maps exist in very strict $CD(K,\infty)$ spaces despite plan uniqueness issues.

Abstract shows entropy and convexity definitions of very strict $CD(K,N)$ spaces are equivalent.

The study presents examples of $CD(0,N)$ spaces with varying dimensions and discusses the limitations of the $CD(0,N)$ condition.

Proposes a new metric space example showing non-constant topological dimension.

Using techniques of optimal transportation and gradient flows in metric spaces, we extend the notion of Riemannian Curvature Dimension condition $RCD(K,\infty)$ introduced (in case the reference measure is finite) by Giuseppe Savare', the first and the second author, to the case the reference measure is $σ$-finite; in …

Proves metric measure spaces with certain properties are one-dimensional.

The CD equalities were introduced to imply the gradient estimate of laplace operator on graphs. This article is based on the unbounded Laplacians, and finally concludes some equivalent properties of the CD(K,$\infty$)and CD(K,n).

We present a generic framework for parallel coordinate descent (CD) algorithms that includes, as special cases, the original sequential algorithms Cyclic CD and Stochastic CD, as well as the recent parallel Shotgun algorithm. We introduce two novel parallel algorithms that are also special cases---Thread-Greedy CD and …

Paper offers a simple CDS approximation formula with high accuracy.

A new algorithm, Weighted Contrastive Divergence (WCD), improves on Contrastive Divergence (CD) for learning Boltzmann architectures.

Donor-aware scRNA-seq benchmarks improve classification accuracy in inflammatory bowel disease.

Study shows curvature bounds for CD and CAT spaces.

Given any K and N we show that there exists a compact geodesic metric measure space satisfying locally the CD(0,4) condition but failing CD(K,N) globally. The space with this property is a suitable non convex subset of R^2 equipped with the l^\infty-norm and the Lebesgue measure. Combining many such spaces gives a (non…

New methods improve prediction regions for high-dimensional data.

This paper uses SLT to ensure learning guarantees in CD detection.

Study uncovers CDS anomalies leading to arbitrage profits.

This paper is devoted to the analysis of metric measure spaces satisfying locally the curvature-dimension condition CD(K,N) introduced by the second author and also studied by Lott & Villani. We prove that the local version of CD(K,N) is equivalent to a global condition CD*(K,N), slightly weaker than the (usual, global…

Basel III introduces new capital charges for CVA. These charges, and the Basel 2.5 default capital charge can be mitigated by CDS. Therefore, to price in the capital relief that CDS contracts provide, we introduce a CDS pricing model with three legs: premium; default protection; and capital relief. If markets are compl…

Estimating the log-likelihood gradient with respect to the parameters of a Restricted Boltzmann Machine (RBM) typically requires sampling using Markov Chain Monte Carlo (MCMC) techniques. To save computation time, the Markov chains are only run for a small number of steps, which leads to a biased estimate. This bias ca…

Quantum annealer speeds up RBM training for image classification.

Regulators require financial institutions to estimate counterparty default risks from liquid CDS quotes for the valuation and risk management of OTC derivatives. However, the vast majority of counterparties do not have liquid CDS quotes and need proxy CDS rates. Existing methods cannot account for counterparty-specific…

Almost-Riemannian manifolds fail to meet a synthetic curvature condition.

Uniform bounds on ends for non-branching CD spaces with nonnegative curvature outside a compact set.

We study insolvency cascades in an interbank system when banks are allowed to insure their loans with credit default swaps (CDS) sold by other banks. We show that, by properly shifting financial exposures from one institution to another, a CDS market can be designed to rewire the network of interbank exposures in a way…

Differentially private random block coordinate descent improves utility in machine learning.

Model predicts stock returns from CDS spreads, useful for trading.

CDS options allow investors to express a view on spread volatility and obtain a wider range of payoffs than are possible with vanilla CDS. We give a detailed exposition of different types of single-name CDS option, including options with upfront protection payment, recovery options and recovery swaps, and also presents…

Graphs satisfy Li-Yau inequality under $CD(0,n)$ curvature condition.

Study compares CDS databases and finds discrepancies due to various factors.

We review different approaches for measuring the impact of liquidity on CDS prices. We start with reduced form models incorporating liquidity as an additional discount rate. We review Chen, Fabozzi and Sverdlove (2008) and Buhler and Trapp (2006, 2008), adopting different assumptions on how liquidity rates enter the CD…

CD algorithm achieves near-optimal convergence rate for unnormalized models.

We prove generalized lower Ricci bounds for Euclidean and spherical cones over complete Riemannian manifolds. These cones are regarded as complete metric measure spaces. In general, they will be neither manifolds nor Alexandrov spaces. We show that the Euclidean cone over an n-dimensional Riemannian manifold whose Ricc…

New model explains CDS price discrepancies in foreign and domestic economies.

The study proves sub-Riemannian manifolds cannot satisfy $\mathrm{CD}$ conditions unless they are Riemannian.

New model values CDS contracts considering multiple credit risks and collateralization.

Contrastive divergence (CD) is a promising method of inference in high dimensional distributions with intractable normalizing constants, however, the theoretical foundations justifying its use are somewhat shaky. This document proposes a framework for understanding CD inference, how/when it works, and provides multiple…

The curvature-dimension condition fails in sub-Finsler geometry, extending previous results in sub-Riemannian geometry.

Through a long-period analysis of the inter-temporal relations between the French markets for credit default swaps (CDS), shares and bonds between 2001 and 2008, this article shows how a financial innovation like CDS could heighten financial instability. After describing the operating principles of credit derivatives i…

Sharp log-Sobolev inequalities proved for ${\sf CD}(0,N)$ spaces.

In this paper we introduce a parameter dependent class of Krylov-based methods, namely CD, for the solution of symmetric linear systems. We give evidence that in our proposal we generate sequences of conjugate directions, extending some properties of the standard Conjugate Gradient (CG) method, in order to preserve the…

In this paper,we will give an easy example to satisfy that we can not conclude CDE' Inequality just from the CD Inequality.

New group constructed from cube complex properties.

This study examines the interaction between CDS and stock indices, revealing significant short and long-term impacts.

Contrastive Divergence (CD) and Persistent Contrastive Divergence (PCD) are popular methods for training the weights of Restricted Boltzmann Machines. However, both methods use an approximate method for sampling from the model distribution. As a side effect, these approximations yield significantly different biases and…

We study closed three-dimensional Alexandrov spaces with a lower Ricci curvature bound in the $\mathsf{CD}^*(K,N)$ sense, focusing our attention on those with positive or nonnegative Ricci curvature. First, we show that a closed three-dimensional $\mathsf{CD}^*(2,3)$-Alexandrov space must be homeomorphic to a spherical…

In the third part of this series we introduce consistent relative value measures for CDS-Bond basis trades using the bond-implied CDS term structure derived from fitted survival rate curves. We explain why this measure is better than the traditionally used Z-spread or Libor OAS and offer simplified hedging and trading …

Proves rectifiability for specific metric spaces with unique tangents.

Investors optimize equity and CDS trading to mitigate default risk.