Properties of Hierarchical Archimedean Copulas

In this paper we analyse the properties of hierarchical Archimedean copulas. This class is a generalisation of the Archimedean copulas and allows for general non-exchangeable dependency structures. We show that the structure of the copula can be uniquely recovered from all bivariate margins. We derive the distribution of the copula value, which is particularly useful for tests and constructing con¯dence intervals. Furthermore, we analyse dependence orderings, multivariate dependence measures and extreme value copulas. Special attention we pay to the tail dependencies and derive several tail dependence indices for general hierarchical Archimedean copulas.copula; multivariate distribution; Archimedean copula; stochastic ordering; hierarchical copula

Modeling Dependencies in Finance using Copulae

In this paper we provide a review of copula theory with applications to finance. We illustrate the idea on the bivariate framework and discuss the simple, elliptical and Archimedean classes of copulae. Since the cop- ulae model the dependency structure between random variables, next we explain the link between the copulae and common dependency measures, such as Kendall's tau and Spearman's rho. In the next section the copulae are generalized to the multivariate case. In this general setup we discuss and provide an intensive literature review of estimation and simulation techniques. Separate section is devoted to the goodness-of-fit tests. The importance of copulae in finance we illustrate on the example of asset allocation problems, Value-at-Risk and time series models. The paper is complemented with an extensive simulation study and an application to financial data.Distribution functions, Dimension Reduction, Risk management, Statistical models

Solving a Production and Inventory Model with a Minimum Lot Size Constrain

The paper deals with the analysis of a special dynamic production and inventory model. In this model logical restrictions to fulfill an accepted constant minimal level of the production lot size are incorporated, instead of keeping setup cost in the objective function, as it is common in many other models. Detailed optimality conditions are derived, which make possible the application of a simple dynamic programming recursion procedure. --dynamic production-inventory model,minimum lot size,dynamic programming

The linear dynamic lot size problem with minimum order quantities

This paper continues the analysis of a special uncapacitated single item lot sizing problem where a minimum order quantity restriction, instead of the setup cost, guarantees a certain level of production lots. A detailed analysis of the model and an investigation of the particularities of the cumulative demand structure allowed us to develop a solution algorithm based on the concept of minimal sub-problems. We present an optimal solution to a minimal sub-problem in an explicit form and prove that it serves as a construction block for the optimal solution of the initial problem. The computational tests and the comparison with the published algorithm confirm the efficiency of the solution algorithm developed here. --lot sizing problem,minimum order quantity,dynamic programming

An O(Tˆ3) algorithm for the capacitated lot sizing problem with minimum order quantities

This paper explores a single-item capacitated lot sizing problem with minimum order quantity, which plays the role of minor set-up cost. We work out the necessary and suffcient solvability conditions and apply the general dynamic programming technique to develop an O(T³) exact algorithm that is based on the concept of minimal sub-problems. An investigation of the properties of the optimal solution structure allows us to construct explicit solutions to the obtained sub-problems and prove their optimality. In this way, we reduce the complexity of the algorithm considerably and confirm its efficiency in an extensive computational study. --production planning,capacitated lot sizing problem,single item,minimum order quantities,capacity constraints,dynamic programming

A partial correlation vine based approach for modeling and forecasting multivariate volatility time-series

A novel approach for dynamic modeling and forecasting of realized covariance matrices is proposed. Realized variances and realized correlation matrices are jointly estimated. The one-to-one relationship between a positive definite correlation matrix and its associated set of partial correlations corresponding to any vine specification is used for data transformation. The model components therefore are realized variances as well as realized standard and partial correlations corresponding to a daily log-return series. As such, they have a clear practical interpretation. A method to select a regular vine structure, which allows for parsimonious time-series and dependence modeling of the model components, is introduced. Being algebraically independent the latter do not underlie any algebraic constraint. The proposed model approach is outlined in detail and motivated along with a real data example on six highly liquid stocks. The forecasting performance is evaluated both with respect to statistical precision and in the context of portfolio optimization. Comparisons with Cholesky decomposition based benchmark models support the excellent prediction ability of the proposed model approach

Properties of Hierarchical Archimedean Copulas

In this paper we analyse the properties of hierarchical Archimedean copulas. This class is a generalisation of the Archimedean opulas and allows for general non-exchangeable dependency structures. We show that the structure of the copula can be uniquely recovered from all bivariate margins. We derive the distribution of the copula value, which is particularly useful for tests and constructing confidence intervals. Furthermore, we analyse dependence orderings, multivariate dependence measures and extreme value copulas. Special attention we pay to the tail dependencies and derive several tail dependence indices for general hierarchical Archimedean copulas