It is well known that Expected Shortfall (also called Average Value-at-Risk) is a convex risk measure, i. e. Expected Shortfall of a convex linear combination of arbitrary risk positions is not greater than a convex linear combination with the same weights of Expected Shortfalls of the same risk positions. In this shor…
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48 results for “linear shortfall”
Investigates risk measures for DC pension decumulation.
problem Develop optimal decumulation strategies for DC plan holders.
method Formulates decumulation as a control problem, studies risk measures (expected shortfall, linear shortfall, probability of shortfall).
result Optimal controls for expected reward and expected shortfall are identical to those for expected reward and linear shortfall.
Investigates a new measure PELVE_n for risk assessment.
problem Estimating higher-order risk measures in finance.
method Mathematical analysis and distribution-specific calculations.
result Developed and analyzed PELVE_n for various distributions.
In this paper, we generalize the parametric delta-VaR method from portfolios with normally distributed risk factors to portfolios with elliptically distributed ones. We treat both the expected shortfall and the Value-at-Risk of such portfolios. Special attention is given to the particular case of a multivariate t-distr…
Minimizing Shortfallq-fin.PM
This paper describes an empirical study of shortfall optimization with Barra Extreme Risk. We compare minimum shortfall to minimum variance portfolios in the US, UK, and Japanese equity markets using Barra Style Factors (Value, Growth, Momentum, etc.). We show that minimizing shortfall generally improves performance ov…
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 variables in the combination. It turns out that under suitable conditions on the join…
We address the problem of portfolio optimization under the simplest coherent risk measure, i.e. the expected shortfall. As it is well known, one can map this problem into a linear programming setting. For some values of the external parameters, when the available time series is too short, the portfolio optimization is …
Simplifies study of multivariate shortfall risk measures.
problem Complexity in studying multivariate shortfall risk measures.
method Defines shortfall risk measures through a 1-dimensional function.
result Simplifies properties of multivariate shortfall risk measures.
Expectile bears some interesting properties in comparison to the industry wide expected shortfall in terms of assessment of tail risk. We study the relationship between expectile and expected shortfall using duality results and the link to optimized certainty equivalent. Lower and upper bounds of expectile are derived …
New AI models improve financial hedging by reducing shortfall and tail risk.
problem Static model calibration gaps in derivatives markets.
method Two reinforcement learning frameworks: RLOP and QLBS.
result RLOP reduces shortfall frequency and improves tail risk in stress scenarios.
We solve the problem of optimal liquidation with volume weighted average price (VWAP) benchmark when the market impact is linear and transient. Our setting is indeed more general as it considers the case when the trading interval is not necessarily coincident with the benchmark interval: Implementation Shortfall and Ta…
We offer a simplified proof for Expected Shortfall's dual representation.
problem The dual representation of Expected Shortfall.
method Basic properties of quantile functions.
result New proof of Expected Shortfall's subadditivity.
The paper calculates bounds for risk metrics and entropies under partial information constraints.
problem Analyzing risk metrics and entropies for unimodal, symmetric distributions with limited information.
method Develops lower and upper bounds for worst-case distortion riskmetrics and weighted entropy for unimodal, symmetric distributions with known mean and variance.
result Sharp upper bounds for distortion riskmetrics and weighted entropy for symmetric distributions.
Adjusted Expected Shortfallq-fin.RM
We refine Expected Shortfall by controlling different tail portions, offering tailored risk assessments.
problem Risk assessment in financial positions, especially in tail regions.
method Introducing adjusted Expected Shortfall measures that control different tail portions.
result Adjusted Expected Shortfall measures ensure risk does not exceed specified thresholds for various probability levels.
The expectile can be considered as a generalization of quantile. While expected shortfall is a quantile based risk measure, we study its counterpart -- the expectile based expected shortfall -- where expectile takes the place of quantile. We provide its dual representation in terms of Bochner integral. Among other prop…
New tests for VaR and ES forecast encompassing using flexible link functions.
problem Testing forecast encompassing for Value at Risk and Expected Shortfall.
method Flexible link functions for testing convex forecast combinations and nonstandard asymptotic theory for boundary parameters.
result Tests based on new link functions outperform unrestricted linear link functions for one-step and multi-step forecasts.
Algorithm reduces historical expected shortfall computation by focusing on worst-case scenarios.
problem Computing the historical expected shortfall efficiently and accurately.
method Multi-step algorithm using Monte Carlo simulations to identify and reduce the number of worst-case scenarios.
result Non-asymptotic bounds for the L p-error of the expected shortfall estimator are derived.
Optimal retirement timing and consumption under shortfall risk management
problem Optimal portfolio, consumption, and endogenous early retirement problem
method Maximizing expected lifetime consumption utility while managing the maximum wealth shortfall relative to a benchmark
result Geometric structure of the stopping set and feedback-form optimal retirement boundary
The paper analyzes worst-case distortion risk metrics and weighted entropy under partial information.
problem Analyzing worst-case distortion risk metrics and weighted entropy with limited information.
method General distributions, partial information (mean and variance), various entropies and risk measures.
result Provides worst-case results for distortion risk metrics and weighted entropy.
This paper introduces new risk measures for evaluating losses with varying time horizons.
problem Capturing horizon risk and cash non-additivity in risk evaluation.
method Uses BSDEs and shortfall approaches to develop h-generalized shortfall risk measures.
result Introduces hq-entropic risk measures as a new family of fully-dynamic risk measures.
The paper calculates MES bounds for systemic risk contributions under uncertain dependence.
problem Measuring systemic risk contributions of financial firms under uncertainty in dependence structure.
method Derives worst-case and best-case bounds for MES under known individual firm risks and partial dependence information.
result Improved MES bounds derived for various types of dependence models.
We prove existence of a self-financing strategy which minimizes shortfall for game options in discrete time
Study asymptotic properties of generalized shortfall risk measures for heavy-tailed risks.
problem Understanding risk measures for heavy-tailed risks.
method Derive asymptotic expansions for generalized shortfall risk measures.
result Unified theory for risk measures including distortion and utility-based measures.
The problem of estimation error of Expected Shortfall is analyzed, with a view of its introduction as a global regulatory risk measure.
A new formula reveals symmetries between mean excess and ES functions.
problem Optimizing risk measures in financial models.
method Established a reverse ES optimization formula.
result Reveals elegant symmetries and relationships between mean excess and ES functions.
Submodular risk measuresq-fin.RM
Submodularity is studied for convex risk measures, including Expected Shortfall.
problem Characterizing submodularity in convex risk measures.
method Analyzing submodularity properties of law-invariant coherent risk measures, including Expected Shortfall and Value-at-Risk.
result AES is submodular only when it reduces to ES, and empirical analysis shows AES violations are less frequent than VaR and ES violations.
Lambda Expected Shortfallq-fin.MF
Introduces Lambda Expected Shortfall as a risk measure generalizing ES.
problem Lack of a comprehensive risk measure that generalizes ES and Lambda-VaR.
method Introduces Lambda-ES, a new risk measure with explicit formula and properties.
result Lambda-ES is the smallest quasi-convex and law-invariant risk measure dominating Lambda-VaR.
On the coherence of Expected Shortfallcond-mat.stat-mech
Expected Shortfall (ES) in several variants has been proposed as remedy for the defi-ciencies of Value-at-Risk (VaR) which in general is not a coherent risk measure. In fact, most definitions of ES lead to the same results when applied to continuous loss distributions. Differences may appear when the underlying loss di…
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 such portfolios. Special attention is given to the particular case of the mixtur…
We study shortfall risk minimization for American options with path dependent payoffs under proportional transaction costs in the Black--Scholes (BS) model. We show that for this case the shortfall risk is a limit of similar terms in an appropriate sequence of binomial models. We also prove that in the continuous time …
We show that the shortfall risk of binomial approximations of game (Israeli) options converges to the shortfall risk in the corresponding Black--Scholes market considering Lipschitz continuous path-dependent payoffs for both discrete- and continuous-time cases. These results are new also for usual American style option…
We consider the pricing and hedging of exotic options in a model-independent set-up using \emph{shortfall risk and quantiles}. We assume that the marginal distributions at certain times are given. This is tantamount to calibrating the model to call options with discrete set of maturities but a continuum of strikes. In …
A new tail-shape index based on Value at Risk and Expected Shortfall.
problem Measuring and comparing tail behavior of loss distributions.
method Introducing a new -index based on equal level relationships between Value at Risk and Expected Shortfall.
result The -index provides a level-dependent, scale-free measure of upper tail behavior.
Expected Shortfall and Beyondcond-mat
Financial institutions have to allocate so-called "economic capital" in order to guarantee solvency to their clients and counter parties. Mathematically speaking, any methodology of allocating capital is a "risk measure", i.e. a function mapping random variables to the real numbers. Nowadays "value-at-risk", which is d…
New method optimizes risk estimation for financial losses.
problem Estimating expected shortfall risk for heavy-tailed distributions.
method Proposes a novel estimator for expected shortfall robust to data corruption.
result Demonstrates superior performance and robustness compared to classical methods.
Study improves accuracy of risk measures using advanced algorithms.
problem Computing accurate risk measures for financial losses.
method Nested stochastic approximation and multilevel acceleration.
result Established central limit theorems for estimation errors.
We present the Shortfall Deviation Risk (SDR), a risk measure that represents the expected loss that occurs with certain probability penalized by the dispersion of results that are worse than such an expectation. SDR combines Expected Shortfall (ES) and Shortfall Deviation (SD), which we also introduce, contemplating t…
We propose a new backtesting framework for Expected Shortfall that could be used by the regulator. Instead of looking at the estimated capital reserve and the realised cash-flow separately, one could bind them into the secured position, for which risk measurement is much easier. Using this simple concept combined with …
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 in finitely many steps. The methods are illustrated by numerical examples.
New methods estimate multivariate shortfall risk more efficiently.
problem Estimating multivariate shortfall risk is computationally challenging.
method Combines Fourier inversion and RQMC sampling in frequency domain.
result Fourier RQMC methods outperform existing benchmarks.
CAESar improves risk forecasting by combining VaR and ES estimates.
problem Lack of tail risk measures in financial risk management.
method Conditional Autoregressive Expected Shortfall model, combining VaR and ES estimates.
result CAESar outperforms existing methods in risk forecasting.
The contour map of estimation error of Expected Shortfall (ES) is constructed. It allows one to quantitatively determine the sample size (the length of the time series) required by the optimization under ES of large institutional portfolios for a given size of the portfolio, at a given confidence level and a given esti…
The issue of constructing a risk minimizing hedge under an additional almost-surely type constraint on the shortfall profile is examined. Several classical risk minimizing problems are adapted to the new setting and solved. In particular, the bankruptcy threat of optimal strategies appearing in the classical risk minim…
A new method tests Expected Shortfall by analyzing both duration and severity of VaR violations.
problem Lack of separate testing for frequency and severity in ES backtesting.
method Uses bivariate orthogonal polynomials to derive moment conditions for durations and severities.
result Proposes a Wald test for identifying mis-specified components in ES models.
Combines VaR and ES forecasts for cryptocurrency market risk management.
problem Improving tail risk forecasts in financial markets.
method Proposes semiparametric and parametric combination frameworks.
result Combined forecasts outperform individual VaR and ES forecasts.
Shortfall from Maximum Convexityq-fin.ST
We review the dynamics of the returns of Leveraged Exchange Traded Funds (LETFs) and propose a new measure of realized volatility: Shortfall from Maximum Convexity. We show that SMC has a more intuitive interpretation and provides more statistical information compared to the traditionally used sample standard deviation…
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 recent result of Fissler and Ziegel (2015) that ES is jointly elicitable with Valu…
New risk measures adjust for tail risk inadequacies.
problem Tail risk inadequacy in classical risk measures.
method Developed a family of adjusted risk measures using target risk profiles.
result Analyzed and derived properties of adjusted risk measures.