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IEEE International Conference on Communications (ICC)

作者： Besser, Karl-Ludwig Jorswieck, Eduard A. Tech Univ Carolo Wilhelmina Braunschweig Inst Commun Technol Braunschweig Germany

ISBN: (纸本)9781728171227

Modern applications of wireless communication systems often have strict performance requirements. Due to its random nature, channel fading is one of the most limiting factors to provide such guarantees. Even if knowledge about the statistics of the individual links to each antenna is available, there usually are additional uncertainties, e.g., imperfect channel-state information (CSI) or dependency uncertainty between multiple fading links. In this work, we consider the latter and show that a rearrangement algorithm can be applied to calculate the minimum and maximum ergodic capacity for fast fading channels when only the marginal fading distributions are known but the joint distribution is unknown. The algorithm can be used for any number of channels and supports arbitrary marginal distributions. The results are useful for communication system designers, e.g., using the worst-case ergodic capacity for robust system design.

关键词： Diversity methods Fading channels Joint distributions Ergodic capacity rearrangement algorithm

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A model-free approach to multivariate option pricing

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REVIEW OF DERIVATIVES RESEARCH 2021年第2期24卷 135-155页

作者： Bernard, Carole Bondarenko, Oleg Vanduffel, Steven Grenoble Ecole Management GEM Dept Accounting Law & Finance Grenoble France Vrije Univ Brussel VUB Dept Econ & Polit Sci Ixelles Belgium Univ Illinois Chicago UIC Dept Finance Chicago IL USA

We propose a novel model-free approach to extract a joint multivariate distribution, which is consistent with options written on individual stocks as well as on various available indices. To do so, we first use the market prices of traded options to infer the risk-neutral marginal distributions for the stocks and the linear combinations given by the indices and then apply a new combinatorial algorithm to find a compatible joint distribution. Armed with the joint distribution, we can price general path-independent multivariate options.

关键词： Multivariate option pricing rearrangement algorithm Risk-neutral joint distribution Option-implied dependence Entropy Model uncertainty

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On some synchronization problems with multiple instances

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2022年 400卷 113697-113697页

作者： Cornilly, Dries Puccetti, Giovanni Rueschendorf, Ludger Vanduffel, Steven Asteria Investment Managers SA Rue Rhone 62 CH-1204 Geneva Switzerland Univ Milan Via Conservatorio 7 I-20122 Milan Italy Univ Freiburg Ernst Zermelo Str 1 D-79104 Freiburg Germany Vrije Univ Brussel Pl Laan 2 B-1050 Brussels Belgium

Many classical synchronization problems such as the assembly line crew scheduling problem (ALCS), some data association problems or multisensor tracking problems can be formulated as finding intra-column rearrangements for a single matrix repre-senting costs, distances, similarities or time requirements. In this paper, we consider an extension of these problems to the case of multiple matrices, reflecting various possible instances (scenarios). To approximate optimal rearrangements, we introduce the Block Swapping algorithm (BSA) and a further customization of it that we call the customized Block Swapping algorithm (Cust BSA). A numerical study shows that the two algorithms we propose - in particular Cust BSA - yield high-quality solutions and also deal efficiently with high-dimensional set-ups. (C) 2021 Elsevier B.V. All rights reserved.

关键词： Assembly line crew scheduling (ALCS) Swapping algorithm rearrangement algorithm Multidimensional assignment problems

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MINIMIZATION OF THE FIRST NONZERO EIGENVALUE PROBLEM FOR TWO-PHASE CONDUCTORS WITH NEUMANN BOUNDARY CONDITIONS

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SIAM JOURNAL ON APPLIED MATHEMATICS 2020年第4期80卷 1607-1628页

作者： Kang, Di Choi, Patrick Kao, Chiu-Yen McMaster Univ Dept Math & Stat Hamilton ON L8S 4K1 Canada Claremont Grad Univ Inst Math Sci Claremont CA 91711 USA Claremont McKenna Coll Dept Math Sci Claremont CA 91711 USA

We consider the problem of minimizing the first nonzero eigenvalue of an elliptic operator with Neumann boundary conditions with respect to the distribution of two conducting materials with a prescribed area ratio in a given domain. In one dimension, we show monotone properties of the first nonzero eigenvalue with respect to various parameters and find the optimal distribution of two conducting materials on an interval under the assumption that the region that has lower conductivity is simply connected. On a rectangular domain in two dimensions, we show that the strip configuration of two conducting materials can be a local minimizer. For general domains, we propose a rearrangement algorithm to find the optimal distribution numerically. Many results on various domains are shown to demonstrate the efficiency and robustness of the algorithms. Topological changes of the optimal configurations are discussed on circles, ellipses, annuli, and L-shaped domains.

关键词： two-phase conductor extremal eigenvalue problem rearrangement algorithm Neumann boundary conditions

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Optimal Shape Design for the p-Laplacian Eigenvalue Problem

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JOURNAL OF SCIENTIFIC COMPUTING 2019年第2期78卷 1231-1249页

作者： Mohammadi, Seyyed Abbas Bozorgnia, Farid Voss, Heinrich Univ Yasuj Dept Math Coll Sci Yasuj *** Iran Orebro Univ Sch Sci & Technol Dept Math S-70182 Orebro Sweden Hamburg Univ Technol Inst Math D-21073 Hamburg Germany

In this paper, a shape optimization problem corresponding to the p-Laplacian operator is studied. Given a density function in a rearrangement class generated by a step function, find the density such that the principal eigenvalue is as small as possible. Considering a membrane of known fixed mass and with fixed boundary of prescribed shape consisting of two different materials, our results determine the way to distribute these materials such that the basic frequency of the membrane is minimal. We obtain some qualitative aspects of the optimizer and then we determine nearly optimal sets which are approximations of the minimizer for specific ranges of parameters values. A numerical algorithm is proposed to derive the optimal shape and it is proved that the numerical procedure converges to a local minimizer. Numerical illustrations are provided for different domains to show the efficiency and practical suitability of our approach.

关键词： Eigenvalue optimization p-Laplacian rearrangement algorithm

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Model-free bounds on Value-at-Risk using extreme value information and statistical distances

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INSURANCE MATHEMATICS & ECONOMICS 2019年 86卷 73-83页

作者： Lux, Thibaut Papapantoleon, Antonis Vrije Univ Brussel Dept Finance Pleinlaan 2 B-1050 Brussels Belgium Natl Tech Univ Athens Dept Math Zografou Campus Athens 15780 Greece

We derive bounds on the distribution function, therefore also on the Value-at-Risk, of phi(X) where phi is an aggregation function and X = (X-1, ... , X-d) is a random vector with known marginal distributions and partially known dependence structure. More specifically, we analyze three types of available information on the dependence structure: First, we consider the case where extreme value information, such as the distributions of partial minima and maxima of X, is available. In order to include this information in the computation of Value-at-Risk bounds, we utilize a reduction principle that relates this problem to an optimization problem over a standard Frechet class, which can then be solved by means of the rearrangement algorithm or using analytical results. Second, we assume that the copula of X is known on a subset of its domain, and finally we consider the case where the copula of X lies in the vicinity of a reference copula as measured by a statistical distance. In order to derive Value-at-Risk bounds in the latter situations, we first improve the Frechet-Hoeffding bounds on copulas so as to include this additional information on the dependence structure. Then, we translate the improved Frechet-Hoeffding bounds to bounds on the Value-at-Risk using the so-called improved standard bounds. In numerical examples we illustrate that the additional information typically leads to a significant improvement of the bounds compared to the marginals-only case. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Value-at-Risk bounds Dependence uncertainty Copulas Improved Frechet Hoeffding bounds Distribution of maxima and minima Reduction principle Distance to reference copula rearrangement algorithm

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Extremal spectral gaps for periodic Schrodinger operators

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ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS 2019年第1期25卷 40-40页

作者： Kao, Chiu-Yen Osting, Braxton Claremont Mckenna Coll Dept Math Sci Claremont CA 91711 USA Univ Utah Dept Math Salt Lake City UT 84112 USA

The spectrum of a Schrodinger operator with periodic potential generally consists of bands and gaps. In this paper, for fixed m, we consider the problem of maximizing the gap-to-midgap ratio for the mth spectral gap over the class of potentials which have fixed periodicity and are pointwise bounded above and below. We prove that the potential maximizing the mth gap-to-midgap ratio exists. In one dimension, we prove that the optimal potential attains the pointwise bounds almost everywhere in the domain and is a step-function attaining the imposed minimum and maximum values on exactly m intervals. Optimal potentials are computed numerically using a rearrangement algorithm and are observed to be periodic. In two dimensions, we develop an efficient rearrangement method for this problem based on a semi-definite formulation and apply it to study properties of extremal potentials. We show that, provided a geometric assumption about the maximizer holds, a lattice of disks maximizes the first gap-to-midgap ratio in the infinite contrast limit. Using an explicit parametrization of two-dimensional Bravais lattices, we also consider how the optimal value varies over all equal-volume lattices.

关键词： Schrodinger operator periodic structure optimal design spectral bandgap Bravais lattices rearrangement algorithm

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Negative dependence in matrix arrangement problems

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Annals of Operations Research 2017年 1-22页

作者： Jakobsons, Edgars Wang, Ruodu RiskLab Department of Mathematics ETH Zurich Rämistrasse 101 Zurich 8092 Switzerland Department of Statistics and Actuarial Science University of Waterloo 200 University Ave. W. Waterloo N2L3G1 ON Canada

Minimizing an arrangement increasing (AI) function with a matrix input over intra-column permutations is a difficult optimization problem of a combinatorial nature. Unlike maximization of AI functions (which is achieved by perfect positive dependence, namely, arranging all columns in an increasing order), minimization is a much more challenging problem due to the lack of a universal definition and construction of compensating arrangements in more than two dimensions. We consider AI functions with a special structure, which facilitates finding close-to-optimal solutions by employing the concept of Sigma-countermonotonicity and the (Block) rearrangement algorithm. We show that many classical optimization problems, including stochastic crew scheduling and assembly of reliable systems, have objective functions with this structure, and illustrate with a numerical case study. This paves a path to obtaining approximate solutions for problems that have so far been considered intractable. © 2017 Springer Science+Business Media, LLC, part of Springer Nature

关键词： Archimedean copulas Negative dependence rearrangement algorithm Scheduling Schur-convexity Systems assembly

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How robust is the value-at-risk of credit risk portfolios?

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EUROPEAN JOURNAL OF FINANCE 2017年第6期23卷 507-534页

作者： Bernard, Carole Rueschendorf, Ludger Vanduffel, Steven Yao, Jing Grenoble Ecole Management Dept Accounting Law & Finance 12 Rue Pierre Semard F-38003 Grenoble 01 France Univ Freiburg Dept Math Stochast Eckerstr 1 D-79104 Freiburg Germany Vrije Univ Brussel Dept Econ Pl Laan 2 B-1050 Brussels Belgium

In this paper, we assess the magnitude of model uncertainty of credit risk portfolio models, that is, what is the maximum and minimum value-at-risk (VaR) of a portfolio of risky loans that can be justified given a certain amount of available information. Puccetti and Ruschendorf [2012a. Computation of Sharp Bounds on the Distribution of a Function of Dependent Risks. Journal of Computational and Applied Maths 236, 1833-1840] and Embrechts, Puccetti, and Ruschendorf [2013. Model Uncertainty and VaR Aggregation. Journal of Banking and Finance 37, 2750-2764] propose the rearrangement algorithm (RA) as a general method to approximate VaR bounds when the loss distributions of the different loans are known but not their interdependence (unconstrained bounds). Their numerical results show that the gap between worst-case and best-case VaR is typically very high, a feature that can only be explained by lack of using dependence information. We propose a modification of the RA that makes it possible to approximate sharp VaR bounds when besides the marginal distributions also higher order moments of the aggregate portfolio such as variance and skewness are available as sources of dependence information. A numerical study shows that the use of moment information makes it possible to significantly improve the (unconstrained) VaR bounds. However, VaR assessments of credit portfolios that are performed at high confidence levels (as it is the case in Solvency II and Basel III) remain subject to significant model uncertainty and are not robust.

关键词： rearrangement algorithm moment bounds value-at-risk credit risk portfolio minimum variance

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RBPCP:Visualization on Multi-set High-dimensional Data 2

RBPCP:Visualization on Multi-set High-dimensional Data

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2017 IEEE 2nd International Conference on Big Data Analysis（ICBDA 2017）

作者： Weiqiang Xie Yingmei Wei Hao Ma Xiaolei Du College of Information System and Management National University of Defense Technology

ISBN: (纸本)9781509036202

Due to the prevalence of Multi-set high-dimensional data in the era of big data,visualization and visual analysis of multiple sets of high-dimensional data are critical to the discovery of data *** Coordinates Plot（PCP） is mainly used for visual analysis of different attributes of the same *** classic method for visualization on multi-set high-dimensional data is to use a conventional PCP with superimposition design or multiple PCPs with juxtaposition ***,these methods can’t effectively detect *** propose a median-based rearrangement algorithm for bundled Parallel Coordinates *** on the algorithm,we present Rearranged Bundled Parallel Coordinates Plot（RBPCP） which effectively improves the visual analysis capability of multi-set high-dimensional data and satisfy the aesthetic *** addition,the proposed RBPCP also utilize brushing,mode switch and dynamic axis scaling for the interactive analysis of set relations and hidden patterns.

关键词： parallel coordinates plot rearrangement algorithm high-dimensional data visualization

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