Computation of sharp bounds on the distribution of a function of dependent risks

Puccetti, Giovanni; Rüschendorf, Ludger

doi:10.1016/j.cam.2011.10.015

Cited by 132 publications

(92 citation statements)

References 7 publications

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“…Nevertheless, these bounds have been extensively studied in recent years and partial solutions have been obtained, see Puccetti and Wang [46] for an overview. Most importantly, Puccetti and Rüschendorf [45] introduced the so-called rearrangement algorithm which is a fast procedure to numerically compute the bounds of interest. Under quite restrictive assumptions, analytical bounds can be computed based on the notion of complete mixability, which was introduced in Wang and Wang [54].…”

Section: Introductionmentioning

confidence: 99%

A Review on Ambiguity in Stochastic Portfolio Optimization

Pflug

Pohl

2017

Set-Valued Var. Anal

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In mean-risk portfolio optimization, it is typically assumed that the assets follow a known distribution P 0 , which is estimated from observed data. Aiming at an investment strategy which is robust against possible misspecification of P 0 , the portfolio selection problem is solved with respect to the worst-case distribution within a Wasserstein-neighborhood of P 0 . We review tractable formulations of the portfolio selection problem under model ambiguity, as it is called in the literature. For instance, it is known that high model ambiguity leads to equally-weighted portfolio diversification. However, it often happens that the marginal distributions of the assets can be estimated with high accuracy, whereas the dependence structure between the assets remains ambiguous. This leads to the problem of portfolio selection under dependence uncertainty. We show that in this case portfolio concentration becomes optimal as the uncertainty with respect to the estimated dependence structure increases. Hence, distributionally robust portfolio optimization can have two very distinct implications: Diversification on the one hand and concentration on the other hand.

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Section: Introductionmentioning

confidence: 99%

A Review on Ambiguity in Stochastic Portfolio Optimization

Pflug

Pohl

2017

Set-Valued Var. Anal

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“…Also, the worst case for the total Value@Risk is not attained under comonotonicity but rather in cases where there is a kind of local negative dependence in the upper right corner of the underlying copula (cf. [10] or [4]). A similar negative result holds for an assumed dependence between correlation and diversi cation (cf.…”

Section: Implications For Risk Managementmentioning

confidence: 99%

New copulas based on general partitions-of-unity and their applications to risk management (part II)

Pfeifer

Mändle

Ragulina

2017

Dependence Modeling

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“…We first present the standard RA of Puccetti and Rüschendorf (2012) and Embrechts et al (2013) and show how to modify it to infer the dependence among variables for which the marginal distributions and the distribution of the sum are known. We include the presentation of the algorithms for completeness.…”

Section: Rearrangement Algorithm To Infer Dependencementioning

confidence: 99%

“…In this paper, we study properties of the Block Rearrangement Algorithm (BRA), which generalizes the standard Rearrangement Algorithm (RA) introduced by Puccetti and Rüschendorf (2012) and further developed in Embrechts et al (2013). The RA has applications in various disciplines.…”

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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Computation of sharp bounds on the distribution of a function of dependent risks

Cited by 132 publications

References 7 publications

A Review on Ambiguity in Stochastic Portfolio Optimization

A Review on Ambiguity in Stochastic Portfolio Optimization

New copulas based on general partitions-of-unity and their applications to risk management (part II)

Rearrangement algorithm and maximum entropy

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