On the nonidentifiability property of Archimedean copula models under dependent censoring

In this paper, we prove a peculiar property shared by the Archimedean copula models, that is, different Archimedean copula models with distinct dependent levels can have the same crude survival functions for dependent censored data. This property directly shows the nonidentifiability property of the Archimedean copula models. The proposed procedure is then demonstrated by two examples.     

Modeling electricity spot and futures price dependence: A multifrequency approach

Electricity prices are known to exhibit multifractal properties. We accommodate this finding by investigating multifractal models for electricity prices. In this paper we propose a flexible Copula-MSM (Markov Switching Multifractal) approach for modeling spot and weekly futures price dynamics. By using a conditional copula function, the framework allows us to separately model the dependence structure, while enabling use of multifractal stochastic volatility models to characterize fluctuations in marginal returns. An empirical experiment is carried out using data from Nord Pool. A study of volatility forecasting performance for electricity spot prices reveals that multifractal techniques are a competitive alternative to GARCH models. We also demonstrate how the Copula-MSM model can be employed for finding optimal portfolios, which minimizes the Conditional Value-at-Risk.     

A quantile-copula approach to conditional density estimation

A new kernel-type estimator of the conditional density is proposed. It is based on an efficient quantile transformation of the data. The proposed estimator, which is based on the copula representation, turns out to have a remarkable product form. Its large-sample properties are considered and comparisons in terms of bias and variance are made with competitors based on nonparametric regression. A comparative simulation study is also provided.     

一种构造阿基米德Copula生成元的方法

阿基米德Copula族在经济、金融方面有着重要的应用,它们是由某些单调递减凸函数所生成的一类Copula,这类单调递减的凸函数被称为生成元．不同生成元所生成的阿基米德Copula具有的性质也完全不同．通过g函数,找到了一种通过某些连续的一维分布函数构造阿基米德Copula生成元的方法．另外,讨论了生成元与g函数之间的关系,从而在某些情况下可以扩展阿基米德Copula族．     

乘积阿基米德Copula

在乘法模式下,对阿基米德Copula进行了推广,提出了乘积阿基米德Copula.通过构造两类特殊的乘积阿基米德Copula,举出了若干乘积阿基米德Copula例子,并分析了关于尾部相依性、对称性等方面的性质.最后,在探讨阿基米德Copula和乘积阿基米德Copula的关系中,提出几个值得进一步讨论的问题.     

Archimedean ϕ ‐tolerance graphs

Let ? be a symmetric binary function, positive valued on positive arguments. A graph G = (V,E) is a ?‐tolerance graph if each vertex υ ∈ V can be assigned a closed interval I_υ and a positive tolerance t_υ so that xy ∈ E ? | I_x ∩ I_y|≥ ? (t_x,t_y). An Archimedean function has the property of tending to infinity whenever one of its arguments tends to infinity. Generalizing a known result of [15] for trees, we prove that every graph in a large class (which includes all chordless suns and cacti and the complete bipartite graphs K_2,k) is a ?‐tolerance graph for all Archimedean functions ?. This property does not hold for most graphs. Next, we present the result that every graph G can be represented as a ?_G‐tolerance graph for some Archimedean polynomial ?_G. Finally, we prove that there is a ?universal”? Archimedean function ? ^* such that every graph G is a ?^*‐tolerance graph. © 2002 Wiley Periodicals, Inc. J Graph Theory 41: 179–194, 2002     

On the Best Approximation in Non-Archimedean Normed Linear Spaces

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A mesoscopic Archimedean tiling having a new complexity in an ABC star polymer

The Archimedean tiling (3².4.3.4) is a regular but complex polygonal assembly of equilateral triangles and squares. This tiling pattern with mesoscopic repeating distance has been found for an ABC star‐branched three‐component polymer composed of polyisoprene, polystyrene, and poly(2‐vinylpyridine). In this structure the environment of a molecule splits into multiple sites and two microdomains with different sizes and shapes are formed for one component. This complexity is the first observation in complex polymer systems and can lead to a new type of mesoscale self‐organization. The tiling pattern has been observed for the other materials on much shorter length‐scale; therefore, the experimental fact observed in the present study is demonstrating that the complexity is universal over different hierarchies. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2427–2432, 2005     

Note on ordering and complexity of Platonic and Archimedean polyhedra based on solid angles

The missing values for the solid angles of the two snub semiregular polyhedra have been calculated, and integrated into the whole series of Platonic and Archimedean polyhedra. This is the only criterion which so far gives an unambiguous answer (without any degeneracy leading to posets) on how to order these polyhedra according to their increasing complexity.     

Orderings of coherent systems with randomized dependent components

Consider a general coherent system with independent or dependent components, and assume that the components are randomly chosen from two different stocks, with the components of the first stock having better reliability than the others. Then here we provide sufficient conditions on the component’s lifetimes and on the random numbers of components chosen from the two stocks in order to improve the reliability of the whole system according to different stochastic orders. We also discuss several examples in which such conditions are satisfied and an application to the study of the optimal random allocation of components in series and parallel systems. As a novelty, our study includes the case of coherent systems with dependent components by using basic mathematical tools (and copula theory).