Related papers: Factor risk measures
Factor models are a very efficient way to describe high dimensional vectors of data in terms of a small number of common relevant factors. This problem, which is of fundamental importance in many disciplines, is usually reformulated in…
The moments of random variables are fundamental statistical measures for characterizing the shape of a probability distribution, encompassing metrics such as mean, variance, skewness, and kurtosis. Additionally, the product moments,…
A multivariate quantile regression model with a factor structure is proposed to study data with many responses of interest. The factor structure is allowed to vary with the quantile levels, which makes our framework more flexible than the…
Where machine-learned predictive risk scores inform high-stakes decisions, such as bail and sentencing in criminal justice, fairness has been a serious concern. Recent work has characterized the disparate impact that such risk scores can…
In this paper we analyze a dynamic recursive extension of the (static) notion of a deviation measure and its properties. We study distribution invariant deviation measures and show that the only dynamic deviation measure which is law…
The paper concerns primal and dual representations as well as time consistency of set-valued dynamic risk measures. Set-valued risk measures appear naturally when markets with transaction costs are considered and capital requirements can be…
Factorial designs are frequently used in different fields of science, e.g. psychological, medical or biometric studies. Standard approaches, as the ANOVA $F$-test, make different assumptions on the distribution of the error terms, the…
We propose a risk measurement approach for a risk-averse stochastic problem. We provide results that guarantee that our problem has a solution. We characterize and explore the properties of the argmin as a risk measure and the minimum as a…
Modeling and characterizing multiple factors is perhaps the most important step in achieving excess returns over market benchmarks. Both academia and industry are striving to find new factors that have good explanatory power for future…
The aim of this paper is to study a new methodological framework for systemic risk measures by applying deep learning method as a tool to compute the optimal strategy of capital allocations. Under this new framework, systemic risk measures…
The aim of this paper is to provide several examples of convex risk measures necessary for the application of the general framework for portfolio theory of Maier-Paape and Zhu, presented in Part I of this series (arXiv:1710.04579…
The impact of scientific publications has traditionally been expressed in terms of citation counts. However, scientific activity has moved online over the past decade. To better capture scientific impact in the digital era, a variety of new…
Factor graphs are a ubiquitous tool for multi-source inference in robotics and multi-sensor networks. They allow for heterogeneous measurements from many sources to be concurrently represented as factors in the state posterior distribution,…
The paper investigates the robust distortion risk measure with linear penalty function under distribution uncertainty. The distribution uncertainties are characterized by predetermined moment conditions or constraints on the Wasserstein…
We introduce and study the main properties of a class of convex risk measures that refine Expected Shortfall by simultaneously controlling the expected losses associated with different portions of the tail distribution. The corresponding…
The time value of money is a critical factor not only in risk analysis, but also in insurance and financial applications. In this paper, we consider a special class of set-valued risk statistics by introducing the time value of money. In…
Risk control has become one of the major concern of financial institutions. The need for adequate statistical tools to measure and anticipate the amplitude of the potential moves of financial markets is clearly expressed, in particular for…
Factor analysis is a flexible technique for assessment of multivariate dependence and codependence. Besides being an exploratory tool used to reduce the dimensionality of multivariate data, it allows estimation of common factors that often…
We introduce a new paradigm for risk sharing that generalizes earlier models based on discrete agents and extends them to allow for sharing risk within a continuum of agents. Agents are represented by points of a measure space and have…
Classically, risk is characterized by a point value probability indicating the likelihood of occurrence of an adverse effect. However, there are domains where the attainability of objective numerical risk characterizations is increasingly…