Related papers: Partial Law Invariance and Risk Measures
In this paper, by proposing two new kinds of distributional uncertainty sets, we explore robustness of distortion risk measures against distributional uncertainty. To be precise, we first consider a distributional uncertainty set which is…
We introduce the concept of a risk form, which is a real functional of two arguments: a measurable function on a Polish space and a measure on that space. We generalize the duality theory and the Kusuoka representation to this setting. For…
Considerable literature has been devoted to developing statistical inferential results for risk measures, especially for those that are of the form of L-functionals. However, practical and theoretical considerations have highlighted quite a…
In safety-critical applications, machine learning models should generalize well under worst-case distribution shifts, that is, have a small robust risk. Invariance-based algorithms can provably take advantage of structural assumptions on…
A classical result in risk measure theory states that every coherent risk measure has a dual representation as the supremum of certain expected value over a risk envelope. We study this topic in more detail. The related issues include: 1.…
We introduce a new test for detection of power-law cross-correlations among a pair of time series - the rescaled covariance test. The test is based on a power-law divergence of the covariance of the partial sums of the long-range…
In recent years, there has been a growing interest in information measures that quantify inaccuracy and uncertainty in systems. In this paper, we introduce a novel concept called the Weighted Fractional Cumulative Residual Inaccuracy…
We introduce two kinds of risk measures with respect to some reference probability measure, which both allow for a certain order structure and domination property. Analyzing their relation to each other leads to the question when a certain…
The purpose of this paper is to describe and extend the use of the newly-introduced measure, residual estimation risk. Following the seminal work of Bignozzi and Tsanakas, the quantification of residual estimation risk is proposed in a…
Optimization under uncertainty and risk is indispensable in many practical situations. Our paper addresses stability of optimization problems using composite risk functionals which are subjected to measure perturbations. Our main focus is…
This paper deals with control of partially observable discrete-time stochastic systems. It introduces and studies Markov Decision Processes with Incomplete Information and with semi-uniform Feller transition probabilities. The important…
We study dynamic risk measures in a very general framework enabling to model uncertainty and processes with jumps. We previously showed the existence of a canonical equivalence class of probability measures hidden behind a given set of…
Interpretation of the nonclassical total probability formula arising in some quantum experiments is provided based on stochastic models described by means of a sequence of random vectors changing in the measurement procedures.
Shortfall systemic (multivariate) risk measures $\rho$ defined through an $N$-dimensional multivariate utility function $U$ and random allocations can be represented as classical (one dimensional) shortfall risk measures associated to an…
We study a general risk measure called the generalized shortfall risk measure, which was first introduced in Mao and Cai (2018). It is proposed under the rank-dependent expected utility framework, or equivalently induced from the cumulative…
We develop a non-standard analysis framework for coherent risk measures and their finite-sample analogues, coherent risk estimators, building on recent work of Aichele, Cialenco, Jelito, and Pitera. Coherent risk measures on $L^\infty$ are…
We investigate the application of inconsistency measures to the problem of analysing business rule bases. Due to some intricacies of the domain of business rule bases, a straightforward application is not feasible. We therefore develop some…
This paper introduces a novel framework for assessing risk and decision-making in the presence of uncertainty, the \emph{$\varphi$-Divergence Quadrangle}. This approach expands upon the traditional Risk Quadrangle, a model that quantifies…
It is shown that the axioms for coherent risk measures imply that whenever there is an asset in a portfolio that dominates the others in a given sample (which happens with finite probability even for large samples), then this portfolio…
Reliable calculations of financial risk require that the fat-tailed nature of prices changes is included in risk measures. To this end, a non-Gaussian approach to financial risk management is presented, modeling the power-law tails of the…