scholarly journals A note on $0$-bipolar knots of concordance order two

2018 ◽  
Vol 147 (4) ◽  
pp. 1773-1780
Author(s):  
Wenzhao Chen
Keyword(s):  
Concordance Order

scholarly journals On Minimal Copulas under the Concordance Order

2019 ◽  
Vol 184 (3) ◽  
pp. 762-780 ◽  
Author(s):  
Jae Youn Ahn ◽  
Sebastian Fuchs
Keyword(s):  
Optimization Problems ◽  
Sufficient Conditions ◽  
Necessary Condition ◽  
Negative Dependence ◽  
Kendall’S Tau ◽  
Kendall's Tau ◽  
Minimal Elements ◽  
Measures Of Concordance ◽  
Concordance Order

AbstractIn the present paper, we study extreme negative dependence focussing on the concordance order for copulas. With the absence of a least element for dimensions $$d\ge 3$$d≥3, the set of all minimal elements in the collection of all copulas turns out to be a natural and quite important extreme negative dependence concept. We investigate several sufficient conditions, and we provide a necessary condition for a copula to be minimal. The sufficient conditions are related to the extreme negative dependence concept of d-countermonotonicity and the necessary condition is related to the collection of all copulas minimizing multivariate Kendall’s tau. The concept of minimal copulas has already been proved to be useful in various continuous and concordance order preserving optimization problems including variance minimization and the detection of lower bounds for certain measures of concordance. We substantiate this key role of minimal copulas by showing that every continuous and concordance order preserving functional on copulas is minimized by some minimal copula, and, in the case the continuous functional is even strictly concordance order preserving, it is minimized by minimal copulas only. Applying the above results, we may conclude that every minimizer of Spearman’s rho is also a minimizer of Kendall’s tau.

Zonoids, linear dependence, and size-biased distributions on the simplex

2003 ◽  
Vol 35 (04) ◽  
pp. 871-884 ◽  
Author(s):  
Marco Dall'Aglio ◽  
Marco Scarsini
Keyword(s):  
Random Vector ◽  
Linear Dependence ◽  
Copula Model ◽  
Convex Order ◽  
Dimension 2 ◽  
Concordance Order ◽  
Biased Distribution

The zonoid of a d-dimensional random vector is used as a tool for measuring linear dependence among its components. A preorder of linear dependence is defined through inclusion of the zonoids. The zonoid of a random vector does not characterize its distribution, but it does characterize the size-biased distribution of its compositional variables. This fact will allow a characterization of our linear dependence order in terms of a linear-convex order for the size-biased compositional variables. In dimension 2 the linear dependence preorder will be shown to be weaker than the concordance order. Some examples related to the Marshall-Olkin distribution and to a copula model will be presented, and a class of measures of linear dependence will be proposed.

scholarly journals Improved Fréchet Bounds and Model-Free Pricing of Multi-Asset Options

2011 ◽  
Vol 48 (02) ◽  
pp. 389-403 ◽  
Author(s):  
Peter Tankov
Keyword(s):  
Random Vector ◽  
Partial Information ◽  
Dependence Structure ◽  
Extra Information ◽  
Model Free ◽  
Compute Model ◽  
Concordance Order ◽  
Fréchet Bounds

Improved bounds on the copula of a bivariate random vector are computed when partial information is available, such as the values of the copula on a given subset of [0, 1]2, or the value of a functional of the copula, monotone with respect to the concordance order. These results are then used to compute model-free bounds on the prices of two-asset options which make use of extra information about the dependence structure, such as the price of another two-asset option.

scholarly journals Impact of Routeing on Correlation Strength in Stationary Queueing Network Processes

2008 ◽  
Vol 45 (03) ◽  
pp. 846-878 ◽  
Author(s):  
Hans Daduna ◽  
Ryszard Szekli
Keyword(s):  
Queueing Networks ◽  
Queueing Network ◽  
Dependence Structure ◽  
Spectral Gaps ◽  
Stochastic Monotonicity ◽  
Closed Queueing Networks ◽  
First Order ◽  
Correlation Strength ◽  
Concordance Order ◽  
Asymptotic Variances

For exponential open and closed queueing networks, we investigate the internal dependence structure, compare the internal dependence for different networks, and discuss the relation of correlation formulae to the existence of spectral gaps and comparison of asymptotic variances. A central prerequisite for the derived theorems is stochastic monotonicity of the networks. The dependence structure of network processes is described by concordance order with respect to various classes of functions. Different networks with the same first-order characteristics are compared with respect to their second-order properties. If a network is perturbed by changing the routeing in a way which holds the routeing equilibrium fixed, the resulting perturbations of the network processes are evaluated.

Zonoids, linear dependence, and size-biased distributions on the simplex

2003 ◽  
Vol 35 (4) ◽  
pp. 871-884 ◽  
Author(s):  
Marco Dall'Aglio ◽  
Marco Scarsini
Keyword(s):  
Random Vector ◽  
Linear Dependence ◽  
Copula Model ◽  
Convex Order ◽  
Dimension 2 ◽  
Concordance Order ◽  
Biased Distribution

The zonoid of a d-dimensional random vector is used as a tool for measuring linear dependence among its components. A preorder of linear dependence is defined through inclusion of the zonoids. The zonoid of a random vector does not characterize its distribution, but it does characterize the size-biased distribution of its compositional variables. This fact will allow a characterization of our linear dependence order in terms of a linear-convex order for the size-biased compositional variables. In dimension 2 the linear dependence preorder will be shown to be weaker than the concordance order. Some examples related to the Marshall-Olkin distribution and to a copula model will be presented, and a class of measures of linear dependence will be proposed.

scholarly journals THE ALGEBRAIC CONCORDANCE ORDER OF A KNOT

2010 ◽  
Vol 19 (12) ◽  
pp. 1693-1711
Author(s):  
CHARLES LIVINGSTON
Keyword(s):  
Infinite Order ◽  
Concordance Order

The algebraic concordance group contains elements of order two, four, and of infinite order. Elements of infinite order are detected by the signature function. This paper develops computable invariants to simplify the computation of the order of torsion classes. The results are applied to determine the algebraic orders of all prime knots of 12 or fewer crossings.

scholarly journals Improved Fréchet Bounds and Model-Free Pricing of Multi-Asset Options

2011 ◽  
Vol 48 (2) ◽  
pp. 389-403 ◽  
Author(s):  
Peter Tankov
Keyword(s):  
Random Vector ◽  
Partial Information ◽  
Dependence Structure ◽  
Extra Information ◽  
Model Free ◽  
Compute Model ◽  
Concordance Order ◽  
Fréchet Bounds

Improved bounds on the copula of a bivariate random vector are computed when partial information is available, such as the values of the copula on a given subset of [0, 1]2, or the value of a functional of the copula, monotone with respect to the concordance order. These results are then used to compute model-free bounds on the prices of two-asset options which make use of extra information about the dependence structure, such as the price of another two-asset option.

scholarly journals New Families of Bivariate Copulas via Unit Lomax Distortion

Risks ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 106
Author(s):  
Fadal Abdullah-A Aldhufairi ◽  
Ranadeera G.M. Samanthi ◽  
Jungsywan H. Sepanski
Keyword(s):  
Random Variable ◽  
Copula Function ◽  
Unit Interval ◽  
Copula Model ◽  
Copula Models ◽  
Density Distributions ◽  
New Family ◽  
Concordance Order ◽  
Bivariate Copula

This article studies a new family of bivariate copulas constructed using the unit-Lomax distortion derived from a transformation of the non-negative Lomax random variable into a variable whose support is the unit interval. Existing copulas play the role of the base copulas that are distorted into new families of copulas with additional parameters, allowing more flexibility and better fit to data. We present general forms for the new bivariate copula function and its conditional and density distributions. The properties of the new family of the unit-Lomax induced copulas, including the tail behaviors, limiting cases in parameters, Kendall’s tau, and concordance order, are investigated for cases when the base copulas are Archimedean, such as the Clayton, Gumbel, and Frank copulas. An empirical application of the proposed copula model is presented. The unit-Lomax distorted copula models outperform the base copulas.

KNOTS OF TEN OR FEWER CROSSINGS OF ALGEBRAIC ORDER 2

2002 ◽  
Vol 11 (02) ◽  
pp. 211-222 ◽  
Author(s):  
ANDRIUS TAMULIS
Keyword(s):  
Alexander Polynomials ◽  
Algebraic Order ◽  
Concordance Order

The concordance orders of many algebraic order two knots of ten or fewer crossings have been heretofore unknown. We use Casson-Gordon invariants and twisted Alexander polynomials to find that, in all but one case, these knots do not have concordance order two. We also find that a certain family of algebraic order two twisted doubles of the unknot have infinite concordance order.

scholarly journals On 3–braid knots of finite concordance order

2017 ◽  
Vol 369 (7) ◽  
pp. 5087-5112
Author(s):  
Paolo Lisca
Keyword(s):  
Concordance Order
Sign in / Sign up

Export Citation Format

Share Document