Related papers: Expected Shortfall: a natural coherent alternative…
In the recent Basel Accords, the Expected Shortfall (ES) replaces the Value-at-Risk (VaR) as the standard risk measure for market risk in the banking sector, making it the most important risk measure in financial regulation. One of the most…
We introduce a semiparametric approach for forecasting Value-at-Risk (VaR) and Expected Shortfall (ES) by modeling the conditional scale of financial returns, defined as the difference between two specified quantiles, via restricted…
The issue related to the quantification of the tail risk of cryptocurrencies is considered in this paper. The statistical methods used in the study are those concerning recent developments in Extreme Value Theory (EVT) for weakly dependent…
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…
The paper discusses capital allocation using the Euler formula and focuses on the risk measures Value-at-Risk (VaR) and Expected shortfall (ES). Some new results connected to this capital allocation is known. Two examples illustrate that…
We introduce an equilibrium asset pricing model, which we build on the relationship between a novel risk measure, the Expected Downside Risk (EDR) and the expected return. On the one hand, our proposed risk measure uses a nonparametric…
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 debate of what quantitative risk measure to choose in practice has mainly focused on the dichotomy between Value at Risk (VaR) -- a quantile -- and Expected Shortfall (ES) -- a tail expectation. Range Value at Risk (RVaR) is a natural…
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…
In general, underestimation of risk is something which should be avoided as far as possible. Especially in financial asset management, equity risk is typically characterized by the measure of portfolio variance, or indirectly by quantities…
We propose forecast encompassing tests for the Expected Shortfall (ES) jointly with the Value at Risk (VaR) based on flexible link (or combination) functions. Our setup allows testing encompassing for convex forecast combinations and for…
Historical (Stressed-) Value-at-Risk ((S)VAR), and Expected Shortfall (ES), are widely used risk measures in regulatory capital and Initial Margin, i.e. funding, computations. However, whilst the definitions of VAR and ES are unambiguous,…
This paper investigates risk measures derived from the expected maximum deficit in a continuous-time framework and develops optimal reserve allocation strategies across multiple lines of business. We formalize the expected maximum deficit…
The investor is interested in the expected return and he is also concerned about the risk and the uncertainty assumed by the investment. One of the most popular concepts used to measure the risk and the uncertainty is the variance and/or…
We develop a statistical framework for risk estimation, inspired by the axiomatic theory of risk measures. Coherent risk estimators -- functionals of P\&L samples inheriting the economic properties of risk measures -- are defined and…
This paper attempts to provide a decision-theoretic foundation for the measurement of economic tail risk, which is not only closely related to utility theory but also relevant to statistical model uncertainty. The main result is that the…
We introduce the resilience rate as a measure of financial resilience. It captures the expected rate at which a dynamic risk measure recovers, i.e., bounces back, when the risk-acceptance set is breached. We develop the corresponding…
Investors who optimize their portfolios under any of the coherent risk measures are naturally led to regularized portfolio optimization when they take into account the impact their trades make on the market. We show here that the impact…
The standard theory of coherent risk measures fails to consider individual institutions as part of a system which might itself experience instability and spread new sources of risk to the market participants. In compliance with an approach…
In this paper we propose a multivariate quantile regression framework to forecast Value at Risk (VaR) and Expected Shortfall (ES) of multiple financial assets simultaneously, extending Taylor (2019). We generalize the Multivariate…