{"title":"A note on bivariate Archimax copulas","authors":"F. Durante, J. F. Sánchez, C. Sempi","doi":"10.1515/demo-2018-0011","DOIUrl":"https://doi.org/10.1515/demo-2018-0011","url":null,"abstract":"Abstract We present an analytical proof of the characterisation of bivariate Archimax copulas in terms of the properties of their generating functions.","PeriodicalId":43690,"journal":{"name":"Dependence Modeling","volume":"6 1","pages":"178 - 182"},"PeriodicalIF":0.7,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/demo-2018-0011","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45312791","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Exponential inequalities for nonstationary Markov chains","authors":"Pierre Alquier, P. Doukhan, Xiequan Fan","doi":"10.1515/demo-2019-0007","DOIUrl":"https://doi.org/10.1515/demo-2019-0007","url":null,"abstract":"Abstract Exponential inequalities are main tools in machine learning theory. To prove exponential inequalities for non i.i.d random variables allows to extend many learning techniques to these variables. Indeed, much work has been done both on inequalities and learning theory for time series, in the past 15 years. However, for the non independent case, almost all the results concern stationary time series. This excludes many important applications: for example any series with a periodic behaviour is nonstationary. In this paper, we extend the basic tools of [19] to nonstationary Markov chains. As an application, we provide a Bernsteintype inequality, and we deduce risk bounds for the prediction of periodic autoregressive processes with an unknown period.","PeriodicalId":43690,"journal":{"name":"Dependence Modeling","volume":"7 1","pages":"150 - 168"},"PeriodicalIF":0.7,"publicationDate":"2018-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/demo-2019-0007","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43930744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On a class of norms generated by nonnegative integrable distributions","authors":"M. Falk, G. Stupfler","doi":"10.1515/demo-2019-0014","DOIUrl":"https://doi.org/10.1515/demo-2019-0014","url":null,"abstract":"Abstract We show that any distribution function on ℝd with nonnegative, nonzero and integrable marginal distributions can be characterized by a norm on ℝd+1, called F-norm. We characterize the set of F-norms and prove that pointwise convergence of a sequence of F-norms to an F-norm is equivalent to convergence of the pertaining distribution functions in the Wasserstein metric. On the statistical side, an F-norm can easily be estimated by an empirical F-norm, whose consistency and weak convergence we establish. The concept of F-norms can be extended to arbitrary random vectors under suitable integrability conditions fulfilled by, for instance, normal distributions. The set of F-norms is endowed with a semigroup operation which, in this context, corresponds to ordinary convolution of the underlying distributions. Limiting results such as the central limit theorem can then be formulated in terms of pointwise convergence of products of F-norms. We conclude by showing how, using the geometry of F-norms, we may characterize nonnegative integrable distributions in ℝd by simple compact sets in ℝd+1. We then relate convergence of those distributions in the Wasserstein metric to convergence of these characteristic sets with respect to Hausdorff distances.","PeriodicalId":43690,"journal":{"name":"Dependence Modeling","volume":"7 1","pages":"259 - 278"},"PeriodicalIF":0.7,"publicationDate":"2018-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/demo-2019-0014","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41540190","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Predictive analytics of insurance claims using multivariate decision trees","authors":"Zhiyu Quan, Emiliano A. Valdez","doi":"10.1515/demo-2018-0022","DOIUrl":"https://doi.org/10.1515/demo-2018-0022","url":null,"abstract":"Abstract Because of its many advantages, the use of decision trees has become an increasingly popular alternative predictive tool for building classification and regression models. Its origins date back for about five decades where the algorithm can be broadly described by repeatedly partitioning the regions of the explanatory variables and thereby creating a tree-based model for predicting the response. Innovations to the original methods, such as random forests and gradient boosting, have further improved the capabilities of using decision trees as a predictive model. In addition, the extension of using decision trees with multivariate response variables started to develop and it is the purpose of this paper to apply multivariate tree models to insurance claims data with correlated responses. This extension to multivariate response variables inherits several advantages of the univariate decision tree models such as distribution-free feature, ability to rank essential explanatory variables, and high predictive accuracy, to name a few. To illustrate the approach, we analyze a dataset drawn from the Wisconsin Local Government Property Insurance Fund (LGPIF)which offers multi-line insurance coverage of property, motor vehicle, and contractors’ equipments.With multivariate tree models, we are able to capture the inherent relationship among the response variables and we find that the marginal predictive model based on multivariate trees is an improvement in prediction accuracy from that based on simply the univariate trees.","PeriodicalId":43690,"journal":{"name":"Dependence Modeling","volume":"6 1","pages":"377 - 407"},"PeriodicalIF":0.7,"publicationDate":"2018-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/demo-2018-0022","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48752020","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Constructions of copulas with given diagonal (and opposite diagonal) sections and some generalizations","authors":"J. Fernández-Sánchez, Manuel Úbeda-Flores","doi":"10.1515/demo-2018-0009","DOIUrl":"https://doi.org/10.1515/demo-2018-0009","url":null,"abstract":"Abstract We review various methods for constructing bivariate copulas with given diagonal sections from seminal work to the most recent research on copulas with given diagonal and opposite diagonal sections. A survey on a generalization of copulas with given diagonal plane sections in higher dimensions and other sections that generalize the diagonal and opposite diagonal sections is of particular interest.","PeriodicalId":43690,"journal":{"name":"Dependence Modeling","volume":"6 1","pages":"139 - 155"},"PeriodicalIF":0.7,"publicationDate":"2018-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/demo-2018-0009","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44570718","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A generalized class of correlated run shock models","authors":"Femin Yalçin, S. Eryilmaz, Ali Riza Bozbulut","doi":"10.1515/demo-2018-0008","DOIUrl":"https://doi.org/10.1515/demo-2018-0008","url":null,"abstract":"Abstract In this paper, a generalized class of run shock models associated with a bivariate sequence {(Xi, Yi)}i≥1 of correlated random variables is defined and studied. For a system that is subject to shocks of random magnitudes X1, X2, ... over time, let the random variables Y1, Y2, ... denote times between arrivals of successive shocks. The lifetime of the system under this class is defined through a compound random variable T = ∑Nt=1 Yt , where N is a stopping time for the sequence {Xi}i≤1 and represents the number of shocks that causes failure of the system. Another random variable of interest is the maximum shock size up to N, i.e. M = max {Xi, 1≤i≤ N}. Distributions of T and M are investigated when N has a phase-type distribution.","PeriodicalId":43690,"journal":{"name":"Dependence Modeling","volume":"6 1","pages":"131 - 138"},"PeriodicalIF":0.7,"publicationDate":"2018-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/demo-2018-0008","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49292729","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Portfolio selection based on graphs: Does it align with Markowitz-optimal portfolios?","authors":"Amelie Hüttner, Jan-Frederik Mai, S. Mineo","doi":"10.1515/demo-2018-0004","DOIUrl":"https://doi.org/10.1515/demo-2018-0004","url":null,"abstract":"Abstract Some empirical studies suggest that the computation of certain graph structures from a (large) historical correlation matrix can be helpful in portfolio selection. In particular, a repeated finding is that information about the portfolio weights in the minimum variance portfolio (MVP) from classical Markowitz theory can be inferred from measurements of centrality in such graph structures. The present article compares the two concepts from a purely algebraic perspective. It is demonstrated that this heuristic relationship between graph centrality and the MVP does not originate from a structural similarity between the two portfolio selection mechanisms, but instead is due to specific features of observed correlation matrices. This means that empirically found relations between both concepts depend critically on the underlying historical data. Repeated empirical evidence for a strong relationship is hence shown to constitute a stylized fact of financial return time series.","PeriodicalId":43690,"journal":{"name":"Dependence Modeling","volume":"6 1","pages":"63 - 87"},"PeriodicalIF":0.7,"publicationDate":"2018-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/demo-2018-0004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41419492","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The strong Fatou property of risk measures","authors":"Shengzhong Chen, N. Gao, F. Xanthos","doi":"10.1515/demo-2018-0012","DOIUrl":"https://doi.org/10.1515/demo-2018-0012","url":null,"abstract":"Abstract In this paper, we explore several Fatou-type properties of risk measures. The paper continues to reveal that the strong Fatou property,whichwas introduced in [19], seems to be most suitable to ensure nice dual representations of risk measures. Our main result asserts that every quasiconvex law-invariant functional on a rearrangement invariant space X with the strong Fatou property is (X, L1) lower semicontinuous and that the converse is true on a wide range of rearrangement invariant spaces. We also study inf-convolutions of law-invariant or surplus-invariant risk measures that preserve the (strong) Fatou property.","PeriodicalId":43690,"journal":{"name":"Dependence Modeling","volume":"6 1","pages":"183 - 196"},"PeriodicalIF":0.7,"publicationDate":"2018-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/demo-2018-0012","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41476552","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Noppadon Kamnitui, J. Fernández-Sánchez, W. Trutschnig
{"title":"Maximum asymmetry of copulas revisited","authors":"Noppadon Kamnitui, J. Fernández-Sánchez, W. Trutschnig","doi":"10.1515/demo-2018-0003","DOIUrl":"https://doi.org/10.1515/demo-2018-0003","url":null,"abstract":"Abstract Motivated by the nice characterization of copulas A for which d∞(A, At) is maximal as established independently by Nelsen [11] and Klement & Mesiar [7], we study maximum asymmetry with respect to the conditioning-based metric D1 going back to Trutschnig [12]. Despite the fact that D1(A, At) is generally not straightforward to calculate, it is possible to provide both, a characterization and a handy representation of all copulas A maximizing D1(A, At). This representation is then used to prove the existence of copulas with full support maximizing D1(A, At). A comparison of D1- and d∞-asymmetry including some surprising examples rounds off the paper.","PeriodicalId":43690,"journal":{"name":"Dependence Modeling","volume":"6 1","pages":"47 - 62"},"PeriodicalIF":0.7,"publicationDate":"2018-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/demo-2018-0003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46892660","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
D. Pfeifer, Andreas Mändle, O. Ragulina, C. Girschig
{"title":"New copulas based on general partitions-of-unity (part III) — the continuous case","authors":"D. Pfeifer, Andreas Mändle, O. Ragulina, C. Girschig","doi":"10.1515/demo-2019-0009","DOIUrl":"https://doi.org/10.1515/demo-2019-0009","url":null,"abstract":"Abstract In this paper we discuss a natural extension of infinite discrete partition-of-unity copulas which were recently introduced in the literature to continuous partition of copulas with possible applications in risk management and other fields. We present a general simple algorithm to generate such copulas on the basis of the empirical copula from high-dimensional data sets. In particular, our constructions also allow for an implementation of positive tail dependence which sometimes is a desirable property of copula modelling, in particular for internal models under Solvency II.","PeriodicalId":43690,"journal":{"name":"Dependence Modeling","volume":"7 1","pages":"181 - 201"},"PeriodicalIF":0.7,"publicationDate":"2018-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/demo-2019-0009","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43119734","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}