Related papers: Systemic risk measures with markets volatility
This paper shows how the theory of dynamic risk measures provides viscosity solutions to a family of second-order parabolic partial differential equations, even in the degenerate case. First, motivated by the martingale problem approach of…
In this work we give a comprehensive overview of the time consistency property of dynamic risk and performance measures, focusing on a the discrete time setup. The two key operational concepts used throughout are the notion of the…
We discuss two distinct approaches, for distorting risk measures of sums of dependent random variables, which preserve the property of coherence. The first, based on distorted expectations, operates on the survival function of the sum. The…
Systemic risk measures play a crucial role in analyzing individual losses conditional on extreme system-wide disasters. In this paper, we provide a unified asymptotic treatment for systemic risk measures. First, we classify them into two…
The purpose of this paper is to give a selective survey on recent progress in random metric theory and its applications to conditional risk measures. This paper includes eight sections. Section 1 is a longer introduction, which gives a…
Ensuring safety through set invariance has proven to be a valuable method in various robotics and control applications. This paper introduces a comprehensive framework for the safe probabilistic invariance verification of both discrete- and…
Uncertainties influencing the dynamical systems pose a significant challenge in estimating the achievable performance of a controller aiming to control such uncertain systems. When the uncertainties are of stochastic nature, obtaining hard…
We develop a pseudo maximum likelihood method for latent factor analysis in short panels without imposing sphericity nor Gaussianity. We derive an asymptotically uniformly most powerful invariant test for the number of factors. On a large…
We introduce the concept of partial law invariance, generalizing the concepts of law invariance and probabilistic sophistication widely used in decision theory, as well as statistical and financial applications. This new concept is…
We consider a competitive market with risk-averse participants. We assume that agents' risks are measured by coherent risk measures introduced by Artzner et al. (1999). Fundamental theorems of welfare economics have long established the…
This paper deals with uncertain dynamical systems in which predictions about the future state of a system are assessed by so called pseudomeasures. Two special cases are stochastic dynamical systems, where the pseudomeasure is the…
In this paper, we seek to understand the behavior of dynamical systems that are perturbed by a parameter that changes discretely in time. If we impose certain conditions, we can study certain embedded systems within a hybrid system as…
This paper introduces a novel framework to study default dependence and systemic risk in a financial network that evolves over time. We analyse several indicators of risk, and develop a new latent space model to assess the health of key…
We propose a novel approach in the assessment of a random risk variable $X$ by introducing magnitude-propensity risk measures $(m_X,p_X)$. This bivariate measure intends to account for the dual aspect of risk, where the magnitudes $x$ of…
This paper proposes RiskRank as a joint measure of cyclical and cross-sectional systemic risk. RiskRank is a general-purpose aggregation operator that concurrently accounts for risk levels for individual entities and their…
In this paper, we consider isotropic and stationary max-stable, inverse max-stable and max-mixture processes $X=(X(s))\_{s\in\bR^2}$ and the damage function $\cD\_X^{\nu}= |X|^\nu$ with $0<\nu<1/2$. We study the quantitative behavior of a…
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…
We review the nature of some well-known phenomena such as volatility smiles, convexity adjustments and parallel derivative markets. We propose that the market is incomplete and postulate the existence of intrinsic risks in every contingent…
We address the problem that classical risk measures may not detect the tail risk adequately. This can occur for instance due to averaging when calculating the Expected Shortfall. The current literature proposes the so-called adjusted…
Within the context of risk integration, we introduce in risk measurement stochastic holding period (SHP) models. This is done in order to obtain a `liquidity-adjusted risk measure' characterized by the absence of a fixed time horizon. The…