Journal ArticleDOI
Conditional value-at-risk for general loss distributions
TLDR
Fundamental properties of conditional value-at-risk are derived for loss distributions in finance that can involve discreetness and provides optimization shortcuts which, through linear programming techniques, make practical many large-scale calculations that could otherwise be out of reach.Abstract:
Fundamental properties of conditional value-at-risk (CVaR), as a measure of risk with significant advantages over value-at-risk (VaR), are derived for loss distributions in finance that can involve discreetness. Such distributions are of particular importance in applications because of the prevalence of models based on scenarios and finite sampling. CVaR is able to quantify dangers beyond VaR and moreover it is coherent. It provides optimization short-cuts which, through linear programming techniques, make practical many large-scale calculations that could otherwise be out of reach. The numerical efficiency and stability of such calculations, shown in several case studies, are illustrated further with an example of index tracking.read more
Citations
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Journal ArticleDOI
On the coherence of Expected Shortfall
Carlo Acerbi,Dirk Tasche +1 more
TL;DR: In this paper, the authors compare some of the definitions of expected shortfall, pointing out that there is one which is robust in the sense of yielding a coherent risk measure regardless of the underlying distributions.
Posted Content
On the coherence of Expected Shortfall
Carlo Acerbi,Dirk Tasche +1 more
TL;DR: In this article, the authors compare some of the definitions of Expected Shortfall, pointing out that there is one which is robust in the sense of yielding a coherent risk measure regardless of the underlying distributions.
Journal ArticleDOI
Making and Evaluating Point Forecasts
TL;DR: In this paper, the authors demonstrate that this common practice can lead to grossly misguided inferences, unless the scoring function and the forecasting task are carefully matched, and demonstrate that point forecasting methods are compared by means of an error measure or scoring function, with the absolute error and the squared error being key examples.
Journal ArticleDOI
Spectral measures of risk: A coherent representation of subjective risk aversion
TL;DR: In this article, the authors study a space of coherent risk measures M/ obtained as certain expansions of coherent elementary basis measures and give necessary and sufficient conditions on / for M/ to be a coherent measure.
Journal ArticleDOI
Portfolio optimization with conditional value-at-risk objective and constraints
TL;DR: In this article, a new approach for optimization of Conditional Value-at-Risk (CVaR) was suggested and tested with several applications, and the approach can be used for maximizing expected returns under CVaR constraints.
References
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Journal ArticleDOI
Coherent Measures of Risk
TL;DR: In this paper, the authors present and justify a set of four desirable properties for measures of risk, and call the measures satisfying these properties "coherent", and demonstrate the universality of scenario-based methods for providing coherent measures.
Journal ArticleDOI
Optimization of conditional value-at-risk
R. T. Rockafellar,S Uryasev +1 more
TL;DR: In this paper, a new approach to optimize or hedging a portfolio of financial instruments to reduce risk is presented and tested on applications, which focuses on minimizing Conditional Value-at-Risk (CVaR) rather than minimizing Value at Risk (VaR), but portfolios with low CVaR necessarily have low VaR as well.
BookDOI
Introduction to Stochastic Programming
John R. Birge,Franois Louveaux +1 more
TL;DR: This textbook provides a first course in stochastic programming suitable for students with a basic knowledge of linear programming, elementary analysis, and probability to help students develop an intuition on how to model uncertainty into mathematical problems.
Book
Modelling Extremal Events: for Insurance and Finance
TL;DR: In this article, an approach to Extremes via Point Processes is presented, and statistical methods for Extremal Events are presented. But the approach is limited to time series analysis for heavy-tailed processes.