Related papers: Expected Shortfall as a Tool for Financial Risk Ma…
We introduce a new regression method that relates the mean of an outcome variable to covariates, under the "adverse condition" that a distress variable falls in its tail. This allows to tailor classical mean regressions to adverse…
In several real-world applications involving decision making under uncertainty, the traditional expected value objective may not be suitable, as it may be necessary to control losses in the case of a rare but extreme event. Conditional…
For a linear combination of random variables, fix some confidence level and consider the quantile of the combination at this level. We are interested in the partial derivatives of the quantile with respect to the weights of the random…
Value-at-risk (VaR) has been playing the role of a standard risk measure since its introduction. In practice, the delta-normal approach is usually adopted to approximate the VaR of portfolios with option positions. Its effectiveness,…
We study the feasibility and noise sensitivity of portfolio optimization under some downside risk measures (Value-at-Risk, Expected Shortfall, and semivariance) when they are estimated by fitting a parametric distribution on a finite sample…
The valuation of over-the-counter derivatives is subject to a series of valuation adjustments known as xVA, which pose additional risks for financial institutions. Associated risk measures, such as the value-at-risk of an underlying…
We consider an optimal investment and risk control problem for an insurer under the mean-variance (MV) criterion. By introducing a deterministic auxiliary process defined forward in time, we formulate an alternative time-consistent problem…
The Value-at-Risk (VaR) and the Expected Shortfall (ES) are the two most popular risk measures in banking and insurance regulation. To bridge between the two regulatory risk measures, the Probability Equivalent Level of VaR-ES (PELVE) was…
We consider market players with tail-risk-seeking behaviour as exemplified by the S-shaped utility introduced by Kahneman and Tversky. We argue that risk measures such as value at risk (VaR) and expected shortfall (ES) are ineffective in…
Risk measures for random vectors have been considered in multi-asset markets with transaction costs and financial networks in the literature. While the theory of set-valued risk measures provide an axiomatic framework for assigning to a…
Marginal expected shortfall (MES) is an important measure when assessing and quantifying the contribution of the financial institution to a systemic crisis. In this paper, we propose time-lagged marginal expected shortfall (TMES) as a…
In the present contribution we characterize law determined convex risk measures that have convex level sets at the level of distributions. By relaxing the assumptions in Weber (2006), we show that these risk measures can be identified with…
The processes of the averaged regression quantiles and of their modifications provide useful tools in the regression models when the covariates are not fully under our control. As an application we mention the probabilistic risk assessment…
To provide a comprehensive summary of the tail distribution, the expected shortfall is defined as the average over the tail above (or below) a certain quantile of the distribution. The expected shortfall regression captures the…
Worst-case risk measures refer to the calculation of the largest value for risk measures when only partial information of the underlying distribution is available. For the popular risk measures such as Value-at-Risk (VaR) and Conditional…
This paper investigates an optimal investment problem under the tail Value at Risk (tail VaR, also known as expected shortfall, conditional VaR, average VaR) and portfolio insurance constraints confronted by a defined-contribution pension…
Analytical, free of time consuming Monte Carlo simulations, framework for credit portfolio systematic risk metrics calculations is presented. Techniques are described that allow calculation of portfolio-level systematic risk measures…
We tackle the problem of estimating risk measures of the infinite-horizon discounted cost within a Markov cost process. The risk measures we study include variance, Value-at-Risk (VaR), and Conditional Value-at-Risk (CVaR). First, we show…
The celebrated Expected Shortfall (ES) optimization formula implies that ES at a fixed probability level is the minimum of a linear real function plus a scaled mean excess function. We establish a reverse ES optimization formula, which says…
In this note, we comment on the relevance of elicitability for backtesting risk measure estimates. In particular, we propose the use of Diebold-Mariano tests, and show how they can be implemented for Expected Shortfall (ES), based on the…