Equity portfolio construction and selection using multiobjective mathematical programming

A multi-objective mixed integer programming model for equity portfolio construction and selection is developed in this study, in order to generate the Pareto optimal portfolios, using a novel version of the well known ε-constraint method. Subsequently, an interactive filtering process is also proposed to assist the decision maker in making his/her final choice among the Pareto solutions. The proposed methodology is tested through an application in the Athens Stock Exchange.     

Minimal infeasible constraint sets in convex integer programs

In this paper we investigate certain aspects of infeasibility in convex integer programs, where the constraint functions are defined either as a composition of a convex increasing function with a convex integer valued function of n variables or the sum of similar functions. In particular we are concerned with the problem of an upper bound for the minimal cardinality of the irreducible infeasible subset of constraints defining the model. We prove that for the considered class of functions, every infeasible system of inequality constraints in the convex integer program contains an inconsistent subsystem of cardinality not greater than 2 ⁿ , this way generalizing the well known theorem of Scarf and Bell for linear systems. The latter result allows us to demonstrate that if the considered convex integer problem is bounded below, then there exists a subset of at most 2 ⁿ −1 constraints in the system, such that the minimum of the objective function subject to the inequalities in the reduced subsystem, equals to the minimum of the objective function over the entire system of constraints.     

To the theory of operator monotone and operator convex functions

We prove that a real function is operator monotone (operator convex) if the corresponding monotonicity (convexity) inequalities are valid for some normal state on the algebra of all bounded operators in an infinite-dimensional Hilbert space. We describe the class of convex operator functions with respect to a given von Neumann algebra in dependence of types of direct summands in this algebra. We prove that if a function from ℝ⁺ into ℝ⁺ is monotone with respect to a von Neumann algebra, then it is also operator monotone in the sense of the natural order on the set of positive self-adjoint operators affiliated with this algebra.     

Möbius and triangle semigroups

The purpose of this paper is to describe the structures of the Möbius semigroup induced by the Möbius transformation group (?, SL(2,?)). In particular, we study stabilizer subsemigoups of Möbius semigroup via the triangle semigroup. In this work, we obtained a geometric interpretation of the least contraction coefficient function of the Möbius semigroup via the triangle semigroup and investigated an extension of stabilizer subsemigoups of the Möbius semigroup. Finally, we obtained a factorization of our stabilizer subsemigoups of the Möbius semigroup.     

From image processing to topological modelling with <Emphasis Type="Italic">p</Emphasis>-adic numbers

Encoding the hierarchical structure of images by p-adic numbers allows for image processing and computer vision methods motivated from arithmetic physics. The p-adic Polyakov action leads to the p-adic diffusion equation in low level vision. Hierarchical segmentation provides another way of p-adic encoding. Then a topology on that finite set of p-adic numbers yields a hierarchy of topological models underlying the image. In the case of chain complexes, the chain maps yield conditions for the existence of a hierarchy, and these can be expressed in terms of p-adic integrals. Such a chain complex hierarchy is a special case of a persistence complex from computational topology, where it is used for computing persistence barcodes for shapes. The approach is motivated by the observation that using p-adic numbers often leads to more efficient algorithms than their real or complex counterparts.     

Multivariate Hierarchical Copulas with Shocks

A transformation to obtain new multivariate hierarchical copulas, starting with an arbitrary copula, is introduced. In addition to the hierarchical structure, the presented construction principle explicitly supports singular components. These may be interpreted as the effect of local or global shocks to the underlying random variables. A large spectrum of dependence patterns can be achieved by the presented transformation, which seems promising for practical applications. Moreover, copulas arising from this construction are similarly admissible with respect to analytical tractability and sampling routines as the original copula. Finally, several well-known families of copulas may be interpreted as special cases.     

Cyclotomic Hecke Algebras of <Emphasis Type="Italic">G</Emphasis>(<Emphasis Type="Italic">r</Emphasis>, <Emphasis Type="Italic">p</Emphasis>, <Emphasis Type="Italic">n</Emphasis>)

In this note, we find a monomial basis of the cyclotomic Hecke algebra \({\mathcal{H}_{r,p,n}}\) of G(r,p,n) and show that the Ariki-Koike algebra \({\mathcal{H}_{r,n}}\) is a free module over \({\mathcal{H}_{r,p,n}}\), using the Gröbner-Shirshov basis theory. For each irreducible representation of \({\mathcal{H}_{r,p,n}}\), we give a polynomial basis consisting of linear combinations of the monomials corresponding to cozy tableaux of a given shape.     

A Generalized Quasilinearization Method for Nonlinear Second-Order Impulsive Differential Equations Involving the <Emphasis Type="Italic">p</Emphasis>-Laplacian

Using variational method and lower and upper solutions, we get a generalized quasilinearization method which construct an iterative scheme converging uniformly to a solution of a nonlinear second-order impulsive differential equations involving the p-Laplacian, and converging quadratically when p=2.     

Some new transformations for Bailey pairs and WP-Bailey pairs

We derive several new transformations relating WP-Bailey pairs. We also consider the corresponding transformations relating standard Bailey pairs, and as a consequence, derive some quite general expansions for products of theta functions which can also be expressed as certain types of Lambert series.     

Analysis of the consistency of a mixed integer programming-based multi-category constrained discriminant model

Classification is concerned with the development of rules for the allocation of observations to groups, and is a fundamental problem in machine learning. Much of previous work on classification models investigates two-group discrimination. Multi-category classification is less-often considered due to the tendency of generalizations of two-group models to produce misclassification rates that are higher than desirable. Indeed, producing “good” two-group classification rules is a challenging task for some applications, and producing good multi-category rules is generally more difficult. Additionally, even when the “optimal” classification rule is known, inter-group misclassification rates may be higher than tolerable for a given classification model. We investigate properties of a mixed-integer programming based multi-category classification model that allows for the pre-specification of limits on inter-group misclassification rates. The mechanism by which the limits are satisfied is the use of a reserved judgment region, an artificial category into which observations are placed whose attributes do not sufficiently indicate membership to any particular group. The method is shown to be a consistent estimator of a classification rule with misclassification limits, and performance on simulated and real-world data is demonstrated.