Related papers: Star-shaped acceptability indexes
Systemic risk is the risk that a company- or industry-level risk could trigger a huge collapse of another or even the whole institution. Various systemic risk measures have been proposed in the literature to quantify the domino and…
In this paper, we introduce two alternative extensions of the classical univariate Value-at-Risk (VaR) in a multivariate setting. The two proposed multivariate VaR are vector-valued measures with the same dimension as the underlying risk…
A classic reachability problem for safety of dynamic systems is to compute the set of initial states from which the state trajectory is guaranteed to stay inside a given constraint set over a given time horizon. In this paper, we leverage…
Measures of concordance have been widely used in insurance and risk management to summarize non-linear dependence among risks modeled by random variables, which Pearson's correlation coefficient cannot capture. However, popular measures of…
Optimization of distortion riskmetrics with distributional uncertainty has wide applications in finance and operations research. Distortion riskmetrics include many commonly applied risk measures and deviation measures, which are not…
Similarity metrics are central in the theory of large networks and graph limits. For bounded-degree graphs, the Benjamini--Schramm metric records the distribution of rooted neighbourhoods, while the stronger colored-neighbourhood metric…
We present a Monte Carlo analysis of the recently introduced variability indices $\tau$ (Tompkins 1999) and $I$ (Zhang et al. 2000 & Torres et al. 2001) for $\gamma$-ray sources. We explore different variability criteria and prove that…
Stellar models are calculated in the approximation of a uniform density distribution. Variational method was used for determination of the boundary of a stability loss, for stellar masses in the range from 2 up to $10^5$ $M_{\odot}$. The…
We model a rotating star as a compressible fluid subject to gravitational forces. In almost all the mathematical literature the entropy is considered to be constant. Here we allow it to be variable. We consider a star that steadily rotates…
In many sequential decision-making problems we may want to manage risk by minimizing some measure of variability in rewards in addition to maximizing a standard criterion. Variance related risk measures are among the most common…
Technology firms conduct randomized controlled experiments ("A/B tests") to learn which actions to take to improve business outcomes. In firms with mature experimentation platforms, experimentation programs can consist of many thousands of…
We propose new summary measures of diagnostic test accuracy which can be used as companions to existing diagnostic accuracy measures. Conceptually, our summary measures are tantamount to the so-called Hellinger affinity and we show that…
Measuring model risk is required by regulators on financial and insurance markets. We separate model risk into parameter estimation risk and model specification risk, and we propose expected shortfall type model risk measures applied to…
Let $\rho$ be a general law--invariant convex risk measure, for instance the average value at risk, and let $X$ be a financial loss, that is, a real random variable. In practice, either the true distribution $\mu$ of $X$ is unknown, or the…
The aim of this paper is to study the optimal investment problem by using coherent acceptability indices (CAIs) as a tool to measure the portfolio performance. We call this problem the acceptability maximization. First, we study the…
We introduce and study a new class of generalized convex functions termed star quasiconvex functions. This class includes convex, star-convex, quasiconvex, quasar-convex, and positively homogeneous functions of any degree $p>0$ as special…
In this paper, we develop the lower and upper bounds of worst-case distortion riskmetrics and weighted entropy for unimodal, and symmetric unimodal distributions when mean and variance information are available. We also consider the sharp…
In this work we consider an iterative method for solving the quasi-convex feasibility problem. We firstly introduce the so-called star subgradient projection operator and present some useful properties. We subsequently obtain a convergence…
This paper aims to investigate the thermodynamic formalism of weighted amenable topological pressure for factor maps of amenable group actions. Following the approach of Tsukamoto [\emph{Ergodic Theory Dynam. Syst.} \textbf{43}(2023),…
We introduce the Lyapunov approach to optimal control problems of average risk-sensitive Markov control processes with general risk maps. Motivated by applications in particular to behavioral economics, we consider possibly non-convex risk…