Related papers: Forecast Encompassing Tests for the Expected Short…
Capital allocation is a procedure for quantifying the contribution of each source of risk to aggregated risk. The gradient allocation rule, also known as the Euler principle, is a prevalent rule of capital allocation under which the…
We propose a new class of monetary risk measures for assessing financial and ESG risk. The construction is based on classical shortfall risk measures with loss function replaced by a multi-attribute utility function. We present an extensive…
The estimation of risk measures recently gained a lot of attention, partly because of the backtesting issues of expected shortfall related to elicitability. In this work we shed a new and fundamental light on optimal estimation procedures…
Expected shortfall (ES), also known as conditional value-at-risk, is a widely recognized risk measure that complements value-at-risk by capturing tail-related risks more effectively. Compared with quantile regression, which has been…
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…
Systemic risk is receiving increasing attention in the insurance industry. In this paper, we propose a multi-dimensional L\'{e}vy process-based renewal risk model with heterogeneous insurance claims, where every dimension indicates a…
The entropic risk measure is widely used in high-stakes decision-making across economics, management science, finance, and safety-critical control systems because it captures tail risks associated with uncertain losses. However, when data…
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…
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…
Testing earthquake forecasts is essential to obtain scientific information on forecasting models and sufficient credibility for societal usage. We aim at enhancing the testing phase proposed by the Collaboratory for the Study of Earthquake…
This paper presents analytical solutions to the problem of how to calculate sensible VaR (Value-at-Risk) and ES (Expected Shortfall) contributions in the CreditRisk+ methodology. Via the ES contributions, ES itself can be exactly computed…
This paper presents a novel approach to stochastic economic model predictive control (SEMPC) that minimizes average economic cost while satisfying an empirical expected shortfall (EES) constraint to manage risk. A new scenario-based problem…
We investigate to which extent the relevant features of (static) Systemic Risk Measures can be extended to a conditional setting. After providing a general dual representation result, we analyze in greater detail Conditional Shortfall…
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…
Systemic risk measures were introduced to capture the global risk and the corresponding contagion effects that is generated by an interconnected system of financial institutions. To this purpose, two approaches were suggested. In the first…
The risk of a financial position is usually summarized by a risk measure. As this risk measure has to be estimated from historical data, it is important to be able to verify and compare competing estimation procedures. In statistical…
The joint Value at Risk (VaR) and expected shortfall (ES) quantile regression model of Taylor (2017) is extended via incorporating a realized measure, to drive the tail risk dynamics, as a potentially more efficient driver than daily…
Risk measures for multivariate financial positions are studied in a utility-based framework. Under a certain incomplete preference relation, shortfall and divergence risk measures are defined as the optimal values of specific set…
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…
A method for quantile-based, semi-parametric historical simulation estimation of multiple step ahead Value-at-Risk (VaR) and Expected Shortfall (ES) models is developed. It uses the quantile loss function, analogous to how the…