Related papers: Shortfall Deviation Risk: An alternative to risk m…
We introduce new forecast encompassing tests for the risk measure Expected Shortfall (ES). The ES currently receives much attention through its introduction into the Basel III Accords, which stipulate its use as the primary market risk…
We consider the problem of sufficient dimensionality reduction (SDR), where the high-dimensional observation is transformed to a low-dimensional sub-space in which the information of the observations regarding the label variable is…
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…
This paper introduces novel backtests for the risk measure Expected Shortfall (ES) following the testing idea of Mincer and Zarnowitz (1969). Estimating a regression framework for the ES stand-alone is infeasible, and thus, our tests are…
This paper provides the first and second order derivatives of any risk measures, including VaR and ES for continuous and discrete portfolio loss random variable variables. Also, we give asymptotic results of the first and second order…
In the last five years, expected shortfall (ES) and stressed ES (SES) have become key required regulatory measures of market risk in the banking sector, especially following events such as the global financial crisis. Thus, finding ways to…
The diversification quotient (DQ) is recently introduced for quantifying the degree of diversification of a stochastic portfolio model. It has an axiomatic foundation and can be defined through a parametric class of risk measures. Since the…
Despite their numerous successes, there are many scenarios where adversarial risk metrics do not provide an appropriate measure of robustness. For example, test-time perturbations may occur in a probabilistic manner rather than being…
We derive new approximations for the Value at Risk and the Expected Shortfall at high levels of loss distributions with positive skewness and excess kurtosis, and we describe their precisions for notable ones such as for exponential, Pareto…
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…
Recent advancements in Distributional Reinforcement Learning (DRL) for modeling loss distributions have shown promise in developing hedging strategies in derivatives markets. A common approach in DRL involves learning the quantiles of loss…
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…
Although quantile regression to calculate risk measures has been widely established in the financial literature, when considering data observed at mixed--frequency, an extension is needed. In this paper, a model is suggested built on a…
Background: Under competing risks, the commonly used sub-distribution hazard ratio (SHR) is not easy to interpret clinically and is valid only under the proportional sub-distribution hazard (SDH) assumption. This paper introduces an…
The stochastic variational inequality problem (SVIP) is an equilibrium model that includes random variables and has been widely applied in various fields such as economics and engineering. Expected residual minimization (ERM) is an…
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,…
In economics, insurance and finance, value at risk (VaR) is a widely used measure of the risk of loss on a specific portfolio of financial assets. For a given portfolio, time horizon, and probability $\alpha$, the $100\alpha\%$ VaR is…
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,…
In this paper, we consider a situation where a decision maker's (DM's) risk preference can be described by a spectral risk measure (SRM) but there is not a single SRM which can be used to represent the DM's preferences consistently.…
We propose a numerical recipe for risk evaluation defined by a backward stochastic differential equation. Using dual representation of the risk measure, we convert the risk valuation to a stochastic control problem where the control is a…