A new approach to assessing model risk in high dimensions

Bernard, Carole; Vanduffel, Steven

doi:10.1016/j.jbankfin.2015.03.007

Cited by 64 publications

(21 citation statements)

References 40 publications

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“…Unfortunately, even for two dependent random variables X 1 and X 2 , there is no closed form of the probability distribution of the sum X 1 + X 2 . It is clear that solving this problem is mainly a numerical issue once the joint distribution of X = (X 1 , X 2 , ..., X n ) is completely specified (Bernard & Vanduffel, 2015).…”

Section: Probabilistic Propertiesmentioning

confidence: 99%

The semi-geometric process and some properties

Wang

2017

IMA Journal of Management Mathematics

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The geometric process has been widely applied in reliability engineering and other areas since its introduction. One of its assumptions is that the times between occurrences of events are independent. This assumption is rather restrictive and can limit its application in the real world. This paper extends the geometric process to a new process, which we call the semi-geometric process, by relaxing this assumption. Some probabilistic properties of the process are derived and parameter estimation is described. A numerical example, based on a real-world data set, is used to illustrate the model and validate the estimation methodology.

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Section: Probabilistic Propertiesmentioning

confidence: 99%

The semi-geometric process and some properties

Wang

2017

IMA Journal of Management Mathematics

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“…Embrechts et al (2013) use the RA in quantitative risk management to obtain sharp approximations for the maximum possible Value-at-Risk (VaR) of a portfolio sum of d dependent risks when all marginal distributions are known but no information on dependence is available; see Aas and Puccetti (2014) for a case study. The RA can also be used in situations under which partial information on dependence is available (see Bernard et al 2017a, b;Bernard and Vanduffel 2015). The algorithm has also important applications in operations research.…”

Section: Introductionmentioning

confidence: 99%

Rearrangement algorithm and maximum entropy

2017

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We study properties of the block rearrangement algorithm (BRA) in the context of inferring dependence among variables given their marginal distributions and the distribution of their sum. We show that when all distributions are Gaussian the BRA yields solutions that are "close to each other" and exhibit almost maximum entropy, i.e., the inferred dependence is Gaussian with a correlation matrix that has maximum possible determinant. We provide evidence that, when the distributions are no longer Gaussian, the property of maximum determinant continues to hold. The consequences of these findings are that the BRA can be used as a stable algorithm for inferring a dependence that is economically meaningful.

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“…However, partial dependence information is often available (e.g., through knowledge of the variance of the sum). This case (and thus a possibly smaller dependence uncertainty spread VaR α (L + ) − VaR α (L + )), is studied by [5][6][7][8]21], where the RA also has been shown to be a useful tool.…”

Section: Introductionmentioning

confidence: 99%

Improved algorithms for computing worst Value-at-Risk

Hofert

Memartoluie

Saunders

et al. 2017

Statistics &Amp; Risk Modeling

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Numerical challenges inherent in algorithms for computing worst Value-at-Risk in homogeneous portfolios are identified and solutions as well as words of warning concerning their implementation are provided. Furthermore, both conceptual and computational improvements to the Rearrangement Algorithm for approximating worst Value-at-Risk for portfolios with arbitrary marginal loss distributions are given. In particular, a novel Adaptive Rearrangement Algorithm is introduced and investigated. These algorithms are implemented using the R package qrmtools and may be of interest in any context in which it is required to find columnwise permutations of a matrix such that the minimal (maximal) row sum is maximized (minimized).

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A new approach to assessing model risk in high dimensions

Cited by 64 publications

References 40 publications

The semi-geometric process and some properties

The semi-geometric process and some properties

Rearrangement algorithm and maximum entropy

Improved algorithms for computing worst Value-at-Risk

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