arXiv research

The paper develops a new approach to conditional risk measures using modular convex analysis.

The paper extends static Systemic Risk Measures to a conditional setting.

We axiomatically introduce risk-consistent conditional systemic risk measures defined on multidimensional risks. This class consists of those conditional systemic risk measures which can be decomposed into a state-wise conditional aggregation and a univariate conditional risk measure. Our studies extend known results f…

We consider families of strongly consistent multivariate conditional risk measures. We show that under strong consistency these families admit a decomposition into a conditional aggregation function and a univariate conditional risk measure as introduced Hoffmann et al. (2016). Further, in analogy to the univariate cas…

New conditional risk measures called conditional generalized quantiles defined and characterized.

The paper establishes a connection between different risk measures and their risk contributions.

New conditions prevent gaps in optimal control problems.

To provide a solid analytic foundation for the module approach to conditional risk measures, this paper establishes a complete random convex analysis over random locally convex modules by simultaneously considering the two kinds of topologies (namely the $(\varepsilon,λ)$--topology and the locally $L^0$-- convex topolo…

Measuring conditional independence is one of the important tasks in statistical inference and is fundamental in causal discovery, feature selection, dimensionality reduction, Bayesian network learning, and others. In this work, we explore the connection between conditional independence measures induced by distances on …

A new method quantizes conditional probability measures using deep learning.

New risk measures assess cryptocurrency market vulnerabilities during financial distress.

When dealing with Heston's stochastic volatility model, the change of measure from the subjective measure P to the objective measure Q is usually investigated under the assumption that the Feller condition is satisfied. This paper closes this gap in the literature by deriving sufficient conditions for the existence of …

Study stability of curvature-dimension condition for negative dimensions.

In this paper, we introduce the rich classes of conditional distortion (CoD) risk measures and distortion risk contribution ($Δ$CoD) measures as measures of systemic risk and analyze their properties and representations. The classes include the well-known conditional Value-at-Risk, conditional Expected Shortfall, and r…

The purpose of this paper is to give a selective survey on recent progress in random metric theory and its applications to conditional risk measures. This paper includes eight sections. Section 1 is a longer introduction, which gives a brief introduction to random metric theory, risk measures and conditional risk measu…

This paper deals with multidimensional dynamic risk measures induced by conditional $g$-expectations. A notion of multidimensional $g$-expectation is proposed to provide a multidimensional version of nonlinear expectations. By a technical result on explicit expressions for the comparison theorem, uniqueness theorem and…

Investigates conditional Chisini means and their application to risk measures.

Paper justifies ideal point forecasts as measurable, clarifying conditions for their existence.

Paper investigates conditions for independence of weak gradients on metric spaces.

The tangent space is constructed in sub-Finsler geometry, leading to the failure of the CD condition in 3D-contact manifolds.

New financial model revises risk measure under NA condition.

This paper presents non-parametric estimates of spectral risk measures applied to long and short positions in 5 prominent equity futures contracts. It also compares these to estimates of two popular alternative measures, the Value-at-Risk (VaR) and Expected Shortfall (ES). The spectral risk measures are conditioned on …

We define Conditional quasi concave Performance Measures (CPMs), on random variables bounded from below, to accommodate for additional information. Our notion encompasses a wide variety of cases, from conditional expected utility and certainty equivalent to conditional acceptability indexes. We provide the characteriza…

Improves full conformal prediction for stochastic non-conformity measures.

Unified framework for global and local two-sample conditional distribution testing.

Reframed GES uses a neural conditional dependence measure for consistent causal structure learning.

We give sufficient conditions for a measured length space (X,d,m) to admit local and global Poincare inequalities. We first introduce a condition DM on (X,d,m), defined in terms of transport of measures. We show that DM, along with a doubling condition on m, implies a scale-invariant local Poincare inequality. We show …

We study the stability of several no-arbitrage conditions with respect to absolutely continuous, but not necessarily equivalent, changes of measure. We first consider models based on continuous semimartingales and show that no-arbitrage conditions weaker than NA and NFLVR are always stable. Then, in the context of gene…

Measuring conditional dependencies among the variables of a network is of great interest to many disciplines. This paper studies some shortcomings of the existing dependency measures in detecting direct causal influences or their lack of ability for group selection to capture strong dependencies and accordingly introdu…

Study on conditioning Gaussian measures on nonlinear observations, including representer theorem and mode estimation.

We study convex risk measures describing the upper and lower bounds of a good deal bound, which is a subinterval of a no-arbitrage pricing bound. We call such a convex risk measure a good deal valuation and give a set of equivalent conditions for its existence in terms of market. A good deal valuation is characterized …

Study Bochner formula on metric measure spaces for vanishing Betti numbers.

We offer a new, rigorous approach to conditional mean embeddings without operator constraints.

Paper introduces contribution measures for systemic risk in crypto markets.

Motivated by a classical comparison result of J. C. F. Sturm we introduce a curvature-dimension condition CD(k,N) for general metric measure spaces and variable lower curvature bound k. In the case of non-zero constant lower curvature our approach coincides with the celebrated condition that was proposed by K.-T. Sturm…

Forré introduces a new conditional independence notion for mixed variables.

Develops measures for non-Borel Anosov groups on Furstenberg boundary.

For a given $1$-Lipschitz map $u\colon\mathbb{R}^n\to\mathbb{R}^m$ we define a partition, up to a set of Lebesgue measure zero, of $\mathbb{R}^n$ into maximal closed convex sets such that restriction of $u$ is an isometry on these sets. We consider a disintegration, with respect to this partition, of a log-concave meas…

This paper applies an AR(1)-GARCH (1, 1) process to detail the conditional distributions of the return distributions for the S&P500, FT100, DAX, Hang Seng, and Nikkei225 futures contracts. It then uses the conditional distribution for these contracts to estimate spectral risk measures, which are coherent risk measures …

Paper discusses natural quasiconvexity and its relation to decomposable sums in risk measures.

New vine copula method forecasts portfolio risk measures robust to market downturns.

The study examines stability of metric measure spaces with integral Ricci curvature bounds.

Simple conditions for comonotonic additive risk measures from acceptance sets.

New framework for calculating multivariate risk measures using Wishart process.

The paper proves gradient estimates for nonlinear parabolic equations on smooth metric measure spaces.

The paper introduces a new Wasserstein distance for approximating posteriors in inverse problems.

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…

In this paper we derive variability measures for the conditional probability distributions of a pair of random variables, and we study its application in the inference of causal-effect relationships. We also study the combination of the proposed measures with standard statistical measures in the the framework of the Ch…