The GAEP algorithm for the fast computation of the distribution of a function of dependent random variables

Arbenz, Philipp; Embrechts, Paul; Puccetti, Giovanni

doi:10.1080/17442508.2011.566337

Cited by 15 publications

(6 citation statements)

References 3 publications

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“…For α close to one, tools from rare event simulation become important; see for instance Asmussen and Glynn [17], Chapter VI. For a more geometric approach, useful in lower dimensions, say d ≤ 5, see [18,19].…”

Section: How Superadditive Can Var Be?mentioning

confidence: 99%

“…From Proposition 3, we can see that the interdependence (copula) between the random variables can be set arbitrarily in the lower region of the marginal supports, and only the tail dependence (in a region of probability, 1 − α, in each margin) matters for the worst VaR value. In the tail region, a smallest element in the convex order sense solves these "sup-inf" and "inf-sup" problems, (18) and (19). To be more precise, each of the individual risks are coupled in a way, such that, conditional on their being all large, their sum is concentrated around a constant (ideally, the sum is a constant, but this is not realistic in many cases).…”

Section: Towards the Inhomogeneous Casementioning

confidence: 99%

See 1 more Smart Citation

An Academic Response to Basel 3.5

Embrechts

Puccetti

Rüschendorf

et al. 2014

Risks

Self Cite

229

139

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Recent crises in the financial industry have shown weaknesses in the modeling of Risk-Weighted Assets (RWAs). Relatively minor model changes may lead to substantial changes in the RWA numbers. Similar problems are encountered in the Value-at-Risk (VaR)-aggregation of risks. In this article, we highlight some of the underlying issues, both methodologically, as well as through examples. In particular, we frame this discussion in the context of two recent regulatory documents we refer to as Basel 3.5.

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Section: How Superadditive Can Var Be?mentioning

confidence: 99%

Section: Towards the Inhomogeneous Casementioning

confidence: 99%

An Academic Response to Basel 3.5

Embrechts

Puccetti

Rüschendorf

et al. 2014

Risks

Self Cite

229

139

View full text Add to dashboard Cite

show abstract

“…There are also other algorithms to numerically calculate the joint distribution of n dependent random variables in the literature such as the GAEP algorithm by Arbenz, Embrechts and Pucetti in [80]. However, their method is limited to calculate the joint distribution of 6 marginals and the results seem to be very similar to Monte-Carlo method.…”

Section: Proposed Methodsmentioning

confidence: 99%

“…A fully automatic mechanism to derive the copulas and estimate the extreme value distributions by testing the applicability is needed. Instead of using Monte-Carlo approach which is basically simulating the scope behaviors, other numerical methods such as GAEP algorithm[80] could be used. paramEstsLmomF irM s, paramEstsLmomSelectM s and paramEstsLmomJanneM s parameters are estimated by using lmomgev function.…”

mentioning

confidence: 99%

Hybrid probabilistic timing analysis with Extreme Value Theory and Copulas

BEKDEMIR

Bazlamaçcı

2022

Microprocessors and Microsystems

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The primary challenge of time-critical systems is to ensure that a task completes its execution before its deadline. In order to ensure that the underlying system comply with stringent timing requirements, designers ought to analyze the timing behavior of the software and its sub-components. Worst-Case Execution Time (WCET) represents the maximum length of time an individual software unit takes to execute and is the most essential value for schedulability analysis in safety-critical systems. Recent studies focus on statistical approaches which augments measurement-based timing analysis with probabilistic confidence level by applying stochastic methods.Common approaches either utilize Extreme Value Theory(EVT) for end-to-end measurements or convolution techniques for a group of program units to derive absolute upper distributional bound of the whole program. The former method lacks insurance of path coverage while the latter one suffers from ignoring possible extreme cases of program units. Furthermore, current state-of-the-art convolution method that is being implemented by a commercial WCET analysis tool overestimates the results under the assumption of worst dependence between the basic blocks. v In this thesis, we propose a hybrid probabilistic timing analysis framework based on modeling the program units with EVT to capture extreme cases and Copulas to model the dependency between the units to derive tighter distributional bounds to mitigate the effects of comonotonic assumptions. The proposed framework also offers a way to minimize the instrumentation probe effects which is essential to obtain fine-grained execution time traces on COTS platforms.

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“…For example, we derived bounds on the sum of dependent risks having overlapping marginals (Embrechts & Puccetti, 2009). With Philipp Arbenz, we also developed algorithms for the fast computation of the distribution of a function of dependent random variables (Arbenz et al , 2011; 2012). Later with Ludger Rüschendorf, Giovanni and I exploited the rearrangement algorithm to compute bounds on the best and worst VaR (Embrechts et al , 2013).…”

Section: Exploring New Research Horizonsmentioning

confidence: 99%

A Conversation With Paul Embrechts

Genest

Nešlehová

2020

Int Statistical Rev

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Summary Paul Embrechts was born in Schoten, Belgium, on 3 February 1953. He holds a Licentiaat in Mathematics from Universiteit Antwerpen (1975) and a DSc from Katholieke Universiteit Leuven (1979), where he was also a Research Assistant from 1975 to 1983. He then held a lectureship in Statistics at Imperial College, London (1983–1985) and was a Docent at Limburgs Universitair Centrum, Belgium (1985–1989) before joining ETH Zürich as a Full Professor of Mathematics in 1989, where he remained until his retirement as an Emeritus in 2018. A renowned specialist of extreme‐value theory and quantitative risk management, he authored or coauthored nearly 200 scientific papers and five books, including the highly influential ‘Modelling of Extremal Events for Insurance and Finance’ (Springer, 1997) and ‘Quantitative Risk Management: Concepts, Techniques and Tools’ (Princeton University Press, 2005, 2015). He served in numerous editorial capacities, notably as Editor‐in‐Chief of the ASTIN Bulletin (1996–2005). Praised for his natural leadership and exceptional communication skills, he helped to bridge the gap between academia and industry through the foundation of RiskLab Switzerland and his sustained leadership for nearly 20 years. He gave numerous prestigious invited and keynote lectures worldwide and served as a member of the board of, or consultant for, various banks, insurance companies and international regulatory authorities. His work was recognised through several visiting positions, including at the Oxford‐Man Institute, and many awards. He is, inter alia, an Elected Fellow of the Institute of Mathematical Statistics (1995) and the American Statistical Association (2014), an Honorary Fellow of the Institute and the Faculty of Actuaries (2000), Honorary Member of the Belgian (2010) and French (2015) Institute of Actuaries and was granted four honorary degrees (University of Waterloo, 2007; Heriot‐Watt University, 2011; Université catholique de Louvain, 2012; City, University of London, 2017). The following conversation took place in Paul's office at ETH Zürich, 17–18 December 2018.

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The GAEP algorithm for the fast computation of the distribution of a function of dependent random variables

Cited by 15 publications

References 3 publications

An Academic Response to Basel 3.5

An Academic Response to Basel 3.5

Hybrid probabilistic timing analysis with Extreme Value Theory and Copulas

A Conversation With Paul Embrechts

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