Related papers: Risk measures under model uncertainty: a Bayesian …
We develop a general theory of risk measures that determines the optimal amount of capital to raise and invest in a portfolio of reference traded securities in order to meet a pre-specified regulatory requirement. The distinguishing feature…
In this paper we show that there is a link between approximate Bayesian methods and prior robustness. We show that what is typically recognized as an approximation to the likelihood, either due to the simulated data as in the Approximate…
By means of the techniques of Boolean valued analysis, we provide a transfer principle between duality theory of classical convex risk measures and duality theory of conditional risk measures. Namely, a conditional risk measure can be…
In this paper we study the asymptotic properties of Bayesian multiple testing procedures for a large class of Gaussian scale mixture pri- ors. We study two types of multiple testing risks: a Bayesian risk proposed in Bogdan et al. (2011)…
In this paper, an optimization problem with uncertain constraint coefficients is considered. Possibility theory is used to model the uncertainty. Namely, a joint possibility distribution in constraint coefficient realizations, called…
Uncertainty is prevalent in engineering design, data-driven problems, and decision making broadly. Due to inherent risk-averseness and ambiguity about assumptions, it is common to address uncertainty by formulating and solving conservative…
This survey gives an introduction to monetary measures of risk as monotone and cash additive functions on spaces of univariate random variables. Primal and dual representation results as well as several examples are discussed. Principal…
We introduce a robust belief-based measure of complexity. The idea is that task A is deemed more complex than task B if the probability of solving A correctly is smaller than the probability of solving B correctly regardless of the reward.…
There are various measures of predictive uncertainty in the literature, but their relationships to each other remain unclear. This paper uses a decomposition of statistical pointwise risk into components, associated with different sources…
The new notion of maturity-independent risk measures is introduced and contrasted with the existing risk measurement concepts. It is shown, by means of two examples, one set on a finite probability space and the other in a diffusion…
This paper compares two different frameworks recently introduced in the literature for measuring risk in a multi-period setting. The first corresponds to applying a single coherent risk measure to the cumulative future costs, while the…
A flexible representation of uncertainty that remains within the standard framework of probabilistic measure theory is presented along with a study of its properties. This representation relies on a specific type of outer measure that is…
According to different typologies of activity and priority, risks can assume diverse meanings and it can be assessed in different ways. In general risk is measured in terms of a probability combination of an event (frequency) and its…
We study issues of robustness in the context of Quantitative Risk Management and Optimization. We develop a general methodology for determining whether a given risk measurement related optimization problem is robust, which we call…
Meta-analysis is a statistical method used in evidence synthesis for combining, analyzing and summarizing studies that have the same target endpoint and aims to derive a pooled quantitative estimate using fixed and random effects models or…
Measuring and managing risk has become crucial in modern decision making under stochastic uncertainty. In two-stage stochastic programming, mean risk models are essentially defined by a parametric recourse problem and a quantification of…
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…
Robust models in mathematical finance replace the classical single probability measure by a sufficiently rich set of probability measures on the future states of the world to capture (Knightian) uncertainty about the "right" probabilities…
In this article the issues are discussed with the Bayesian approach, least-square fits, and most-likely fits. Trying to counter these issues, a method, based on weighted confidence, is proposed for estimating probabilities and other…
The framework of this paper is that of risk measuring under uncertainty, which is when no reference probability measure is given. To every regular convex risk measure on ${\cal C}_b(\Omega)$, we associate a unique equivalence class of…