相关论文: Multivariate risks and depth-trimmed regions
In this paper, we will show that under certain conditions, associated to any fixed distortion function $g$, the distortion risk measure of a sum of two counter-monotonic risks can be expressed as the sum of two related distortion risk…
Model uncertainty has been one prominent issue both in the theory of risk measures and in practice such as financial risk management and regulation. Motivated by this observation, in this paper, we take a new perspective to describe the…
This paper proposes the estimation of a mutual shape from a set of different segmentation results using both active contours and information theory. The mutual shape is here defined as a consensus shape estimated from a set of different…
This survey contains a selection of topics unified by the concept of positive semi-definiteness (of matrices or kernels), reflecting natural constraints imposed on discrete data (graphs or networks) or continuous objects (probability or…
Uncertainty in economics still poses some fundamental problems illustrated, e.g., by the Allais and Ellsberg paradoxes. To overcome these difficulties, economists have introduced an interesting distinction between 'risk' and 'ambiguity'…
We discuss two distinct approaches, for distorting risk measures of sums of dependent random variables, which preserve the property of coherence. The first, based on distorted expectations, operates on the survival function of the sum. The…
Systemic risk measures are crucial for the stability of financial markets, yet classical formulations fail to capture the complexity of market volatility. We propose a new framework for systemic risk measurement on the variable-exponent…
For arbitrary two probability measures on real d-space with given means and variances (covariance matrices), we provide lower bounds for their total variation distance. In the one-dimensional case, a tight bound is given.
The numerical range of a matrix is studied geometrically via the cone of positive semidefinite matrices (or semidefinite cone for short). In particular it is shown that the feasible set of a two-dimensional linear matrix inequality (LMI),…
The numerical range of a matrix is studied geometrically via the cone of positive semidefinite matrices (or semidefinite cone for short). In particular it is shown that the feasible set of a two-dimensional linear matrix inequality (LMI),…
In this paper we consider optimization with relaxation, an ample paradigm to make data-driven designs. This approach was previously considered by the same authors of this work in Garatti and Campi (2019), a study that revealed a deep-seated…
As a measure for the centrality of a point in a set of multivariate data, statistical depth functions play important roles in multivariate analysis, because one may conveniently construct descriptive as well as inferential procedures…
We study empirical variants of the halfspace (Tukey) depth of a probability measure $\mu$, which are obtained by replacing $\mu$ with the corresponding weighted empirical measure. We prove analogues of the Marcinkiewicz--Zygmund strong law…
The use of quantiles to obtain insights about multivariate data is addressed. It is argued that incisive insights can be obtained by considering directional quantiles, the quantiles of projections. Directional quantile envelopes are…
We provide an axiomatic approach to the theory of local tangent cones of regular sub-Riemannian manifolds and the differentiability of mappings between such spaces. This axiomatic approach relies on a notion of a dilation structure which is…
Despite decades of research in risk management, most of the literature has focused on scalar risk measures (like e.g. Value-at-Risk and Expected Shortfall). While such scalar measures provide compact and tractable summaries, they provide a…
In order to evaluate the quality of the scientific research, we introduce a new family of scientific performance measures, called Scientific Research Measures (SRM). Our proposal originates from the more recent developments in the theory of…
The halfspace depth is a well studied tool of nonparametric statistics in multivariate spaces, naturally inducing a multivariate generalisation of quantiles. The halfspace depth of a point with respect to a measure is defined as the infimum…
In the second part of our series we suggest new definitions of credit bond duration and convexity that remain consistent across all levels of credit quality including deeply distressed bonds and introduce additional risk measures that are…
We develop an approach to risk classification based on quantile contours and allometric modelling of multivariate anthropometric measurements. We propose the definition of allometric direction tangent to the directional quantile envelope,…