Related papers: What risk measures are time consistent for all fil…
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…
Due to their heterogeneity, insurance risks can be properly described as a mixture of different fixed models, where the weights assigned to each model may be estimated empirically from a sample of available data. If a risk measure is…
This paper is the continuation of "Pricing with coherent risk" and deals with further applications of coherent risk measures to problems of finance. First, we study the optimization problem. Three forms of this problem are considered.…
The main goal of this paper is to investigate under which conditions cash-subadditive convex dynamic risk measures are time-consistent. Proceeding as in Detlefsen and Scandolo \cite{detlef-scandolo} and inspired by their result, we give a…
According to recent results, convergence in a prespecified or prescribed finite time can be achieved under extreme model uncertainty if control is applied continuously over time. This paper shows that this extreme amount of uncertainty…
The paper analyzes risk assessment for cash flows in continuous time using the notion of convex risk measures for processes. By combining a decomposition result for optional measures, and a dual representation of a convex risk measure for…
We consider the problem of discriminating between states of a specified set with maximum confidence. For a set of linearly independent states unambiguous discrimination is possible if we allow for the possibility of an inconclusive result.…
In reliability-based design, the estimation of the failure probability is a crucial objective. However, focusing only on the occurrence of the failure event may be insufficient to entirely characterize the reliability of the considered…
Model risk has a huge impact on any risk measurement procedure and its quantification is therefore a crucial step. In this paper, we introduce three quantitative measures of model risk when choosing a particular reference model within a…
Credit ratings are widely used by investors as a screening device. We introduce and study several natural notions of risk consistency that promote prudent investment decisions in the framework of Choquet rating criteria. Three closely…
We discuss a general strategy to construct coherence measures. One can build an important class of coherence measures which cover the relative entropy measure for pure states, the $l_1$-norm measure for pure states and the $\alpha$-entropy…
Mean-deviation models, along with the existing theory of coherent risk measures, are well studied in the literature. In this paper, we characterize monotonic mean-deviation (risk) measures from a general mean-deviation model by applying a…
A one-to-one correspondence is drawn between law invariant risk measures and divergences, which we define as functionals of pairs of probability measures on arbitrary standard Borel spaces satisfying a few natural properties. Divergences…
We consider the problem of constructing robust nonparametric confidence intervals and tests of hypothesis for the median when the data distribution is unknown and the data may contain a small fraction of contamination. We propose a…
In decision making under uncertainty and risk, worst-case risk assessments are often conducted using maxitive monetary risk measures. In this article, we study maxitive monetary risk measures on the space $L^0$ of all random variables…
Two approaches to time consistency of risk averse multistage stochastic problems were discussed in the recent literature. In one approach certain properties of the cor-responding risk measure are postulated which imply its decomposability.…
The aim of this work is to study risk measures generated by distortion functions in a dynamic discrete time setup, and to investigate the corresponding dynamic coherent acceptability indices (DCAIs) generated by families of such risk…
Dependence among multiple lifetimes is a key factor for pricing and evaluating the risk of joint life insurance products. The dependence structure can be exposed to model uncertainty when available data and information are limited. We…
Procyclicality of historical risk measure estimation means that one tends to over-estimate future risk when present realized volatility is high and vice versa under-estimate future risk when the realized volatility is low. Out of it…
In this paper, we develop a novel unified methodology for performance and robustness analysis of linear dynamical networks. We introduce the notion of systemic measures for the class of first--order linear consensus networks. We classify…