Related papers: On the coherence of Expected Shortfall
Conditional Value-at-Risk (CVaR) is a widely used risk-sensitive objective for learning under rare but high-impact losses, yet its statistical behavior under heavy-tailed data remains poorly understood. Unlike expectation-based risk, CVaR…
Distortion risk measures are extensively used in finance and insurance applications because of their appealing properties. We present three methods to construct new class of distortion functions and measures. The approach involves the…
Maximum drawdown, the largest cumulative loss from peak to trough, is one of the most widely used indicators of risk in the fund management industry, but one of the least developed in the context of measures of risk. We formalize drawdown…
The issue of model risk in default modeling has been known since inception of the Academic literature in the field. However, a rigorous treatment requires a description of all the possible models, and a measure of the distance between a…
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…
This paper applies the Extreme-Value (EV) Generalised Pareto distribution to the extreme tails of the return distributions for the S&P500, FT100, DAX, Hang Seng, and Nikkei225 futures contracts. It then uses tail estimators from these…
Quantification of risk positions under model uncertainty is of crucial importance from both viewpoints of external regulation and internal management. The concept of model uncertainty, sometimes also referred to as model ambiguity. Although…
We study a non-concave optimization problem in which a financial company maximizes the expected utility of the surplus under a risk-based regulatory constraint. For this problem, we consider four different prevalent risk constraints…
We present a computational method for measuring financial risk by estimating the Value at Risk and Expected Shortfall from financial series. We have made two assumptions: First, that the predictive distributions of the values of an asset…
We present the conditional value-at-risk (CVaR) in the context of Markov chains and Markov decision processes with reachability and mean-payoff objectives. CVaR quantifies risk by means of the expectation of the worst p-quantile. As such it…
Marginal expected shortfall is unquestionably one of the most popular systemic risk measures. Studying its extreme behaviour is particularly relevant for risk protection against severe global financial market downturns. In this context,…
Quantiles and expected shortfalls are commonly used risk measures in financial risk management. The two measurements are correlated while have distinguished features. In this project, our primary goal is to develop stable and practical…
Credit Suisse First Boston (CSFB) launched in 1997 the model CreditRisk+ which aims at calculating the loss distribution of a credit portfolio on the basis of a methodology from actuarial mathematics. Knowing the loss distribution, it is…
Expectiles define the only law-invariant, coherent and elicitable risk measure apart from the expectation. The popularity of expectile-based risk measures is steadily growing and their properties have been studied for independent data, but…
Value-at-Risk (VaR) is an institutional measure of risk favored by financial regulators. VaR may be interpreted as a quantile of future portfolio values conditional on the information available, where the most common quantile used is 95%.…
We present a general framework for a comparative theory of variability measures, with a particular focus on the recently introduced one-parameter families of inter-Expected Shortfall differences and inter-expectile differences, that are…
Appropriate risk management is crucial to ensure the competitiveness of financial institutions and the stability of the economy. One widely used financial risk measure is Value-at-Risk (VaR). VaR estimates based on linear and parametric…
Conditional value-at-risk (CoVaR) is one of the most important measures of systemic risk. It is defined as the high quantile conditional on a related variable being extreme, widely used in the field of quantitative risk management. In this…
We provide an elementary proof of the dual representation of Expected Shortfall on the space of integrable random variables over a general probability space. Unlike the results in the extant literature, our proof only exploits basic…
In this paper, we generalize the parametric Delta-VaR methods from portfolios with elliptic distributed risk factors to portfolios with mixture of elliptically distributed ones. We treat both the Expected Shortfall and the Value-at-Risk of…