45 research outputs found
Moments and associated measures of copulas with fractal support
Copulas are closely related to the study of distributions and the dependence between random variables. In this paper we develop a recurrence formula for the moments of a measure associated with a copula (a bivariate distribution function with uniform one-dimensional marginals) in the case that its support is a fractal set. We do the same for its principal and secondary diagonals. We also study certain measures of dependence or association for these copulas with fractal supports
Evolution of the Dependence of Residual Lifetimes
We investigate the dependence properties of a vector of residual lifetimes by means of the copula associated with the conditional distribution function. In particular, the evolution of positive dependence properties (like quadrant dependence and total positivity) are analyzed and expressions for the evolution of measures of association are given
A link between Kendall's tau, the length measure and the surface of bivariate copulas, and a consequence to copulas with self-similar support
Working with shuffles we establish a close link between Kendall's tau, the
so-called length measure, and the surface area of bivariate copulas and derive
some consequences. While it is well-known that Spearman's rho of a bivariate
copula A is a rescaled version of the volume of the area under the graph of A,
in this contribution we show that the other famous concordance measure,
Kendall's tau, allows for a simple geometric interpretation as well - it is
inextricably linked to the surface area of A.Comment: 12 pages, 3 figure
Some Counterexamples in Positive Dependence.
We provide some counterexamples showing that some concepts of positive dependence are strictly stronger than others. In particular we will settle two questions posed by Pemantle (2000) and Pellerey (2002) concerning respectively association versus weak association, weak association versus supermodular dependence, and supermodular dependence versus positive orthant dependence.Association, weak association, supermodular dependence, positive orthant dependence.
Zonoids, Linear Dependence, and Size-Biased Distributions on the Simplex.
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 characterizes 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.zonoid, zonotope, linear dependence, compositional variables, multivariate size biased distribution, concordance order, Marshall-Olkin distribution.
Untangling hotel industry’s inefficiency: An SFA approach applied to a renowned Portuguese hotel chain
The present paper explores the technical efficiency of four hotels from Teixeira Duarte Group - a renowned Portuguese hotel chain. An efficiency ranking is established from these four hotel units located in Portugal using Stochastic Frontier Analysis. This methodology allows to discriminate between measurement error and systematic inefficiencies in the estimation process enabling to investigate the main inefficiency causes. Several suggestions concerning efficiency improvement are undertaken for each hotel studied.info:eu-repo/semantics/publishedVersio
Recommended from our members
Pricing Basket of Credit Default Swaps and Collateralised Debt Obligation by Lévy Linearly Correlated, Stochastically Correlated, and Randomly Loaded Factor Copula Models and Evaluated by the Fast and Very Fast Fourier Transform
In the last decade, a considerable growth has been added to the volume of the credit risk
derivatives market. This growth has been followed by the current financial market
turbulence. These two periods have outlined how significant and important are the
credit derivatives market and its products. Modelling-wise, this growth has parallelised
by more complicated and assembled credit derivatives products such as mth to default
Credit Default Swaps (CDS), m out of n (CDS) and collateralised debt obligation
(CDO).
In this thesis, the Lévy process has been proposed to generalise and overcome the Credit
Risk derivatives standard pricing model's limitations, i.e. Gaussian Factor Copula
Model. One of the most important drawbacks is that it has a lack of tail dependence or,
in other words, it needs more skewed correlation. However, by the Lévy Factor Copula
Model, the microscopic approach of exploring this factor copula models has been
developed and standardised to incorporate an endless number of distribution alternatives
those admits the Lévy process. Since the Lévy process could include a variety of
processes structural assumptions from pure jumps to continuous stochastic, then those
distributions who admit this process could represent asymmetry and fat tails as they
could characterise symmetry and normal tails. As a consequence they could capture
both high and low events¿ probabilities.
Subsequently, other techniques those could enhance the skewness of its correlation and
be incorporated within the Lévy Factor Copula Model has been proposed, i.e. the
'Stochastic Correlated Lévy Factor Copula Model' and 'Lévy Random Factor Loading
Copula Model'. Then the Lévy process has been applied through a number of proposed
Pricing Basket CDS&CDO by Lévy Factor Copula and its skewed versions and evaluated by V-FFT limiting and mixture cases of the Lévy Skew Alpha-Stable distribution and Generalized
Hyperbolic distribution.
Numerically, the characteristic functions of the mth to default CDS's and
(n/m) th to
default CDS's number of defaults, the CDO's cumulative loss, and loss given default
are evaluated by semi-explicit techniques, i.e. via the DFT's Fast form (FFT) and the
proposed Very Fast form (VFFT). This technique through its fast and very fast forms
reduce the computational complexity from O(N2) to, respectively, O(N log2 N ) and
O(N )
Complexity in Economic and Social Systems
There is no term that better describes the essential features of human society than complexity. On various levels, from the decision-making processes of individuals, through to the interactions between individuals leading to the spontaneous formation of groups and social hierarchies, up to the collective, herding processes that reshape whole societies, all these features share the property of irreducibility, i.e., they require a holistic, multi-level approach formed by researchers from different disciplines. This Special Issue aims to collect research studies that, by exploiting the latest advances in physics, economics, complex networks, and data science, make a step towards understanding these economic and social systems. The majority of submissions are devoted to financial market analysis and modeling, including the stock and cryptocurrency markets in the COVID-19 pandemic, systemic risk quantification and control, wealth condensation, the innovation-related performance of companies, and more. Looking more at societies, there are papers that deal with regional development, land speculation, and the-fake news-fighting strategies, the issues which are of central interest in contemporary society. On top of this, one of the contributions proposes a new, improved complexity measure