Using genetic algorithm to solve a new multi-period stochastic optimization model

This paper presents a new asset allocation model based on the CVaR risk measure and transaction costs. Institutional investors manage their strategic asset mix over time to achieve favorable returns subject to various uncertainties, policy and legal constraints, and other requirements. One may use a multi-period portfolio optimization model in order to determine an optimal asset mix. Recently, an alternative stochastic programming model with simulated paths was proposed by Hibiki [N. Hibiki, A hybrid simulation/tree multi-period stochastic programming model for optimal asset allocation, in: H. Takahashi, (Ed.) The Japanese Association of Financial Econometrics and Engineering, JAFFE Journal (2001) 89-119 (in Japanese); N. Hibiki A hybrid simulation/tree stochastic optimization model for dynamic asset allocation, in: B. Scherer (Ed.), Asset and Liability Management Tools: A Handbook for Best Practice, Risk Books, 2003, pp. 269-294], which was called a hybrid model. However, the transaction costs weren’t considered in that paper. In this paper, we improve Hibiki’s model in the following aspects: (1) The risk measure CVaR is introduced to control the wealth loss risk while maximizing the expected utility; (2) Typical market imperfections such as short sale constraints, proportional transaction costs are considered simultaneously. (3) Applying a genetic algorithm to solve the resulting model is discussed in detail. Numerical results show the suitability and feasibility of our methodology.     

A generalization of Voronoi's unit algorithm II

It is proved that the generalized Voronoi algorithm developed in Part I of this paper computes the fundamental units of all fields of unit rank 2, i.e., of the totally real cubic fields, of the quartic fields with two real conjugate fields, of the quintic fields with only one real conjugate field, and of the totally complex sextic fields.     

A generalization of Voronoi's unit algorithm I

By means of a new method of mapping an algebraic number field into a euclidean space Voronoi's unit algorithm is generalized to all algebraic number fields and it is proved that the generalized Voronoi algorithm computes the fundamental units of all algebraic number fields of unit rank 1, i.e., of the real quadratic fields, of the complex cubic fields, and of the totally complex quartic fields.     

Fully Hilbertian fields

We introduce the notion of fully Hilbertian fields, a strictly stronger notion than that of Hilbertian fields. We show that this class of fields exhibits the same good behavior as Hilbertian fields, but for fields of uncountable cardinality, is more natural than the notion of Hilbertian fields. In particular, we show it can be used to achieve stronger Galois theoretic results. Our proofs also provide a step toward the so-called Jarden-Lubotzky twinning principle.     

The structure of harmonizable isotropic random fields

The class of harmonizable processes and fields are a natural extension of the class of stationary processes and fields. Random fields admit an additional property called isotropy. The classical spectral and covariance representations for stationary isotropic random fields are extended to the harmonizable isotropic case. A classification of these fields is obtained based upon the smoothness properties of their covariances. In contrast to the stationary case, it is also shown that there exist non-trivial harmonizable isotropic fields which satisfy the Laplace operator in the L ²-sense     

Quadratic vector fields in ℂP2 with solvable monodromy group at infinity

Quadratic vector fields for which the line at infinity is a phase curve with three different singular points are considered. It is assumed that the characteristic numbers of these singular points are not multiples of 1/4 or 1/6. It is shown that among the fields with fixed characteristic numbers satisfying this assumption, one can choose seven fields such that any other field with solvable noncommutative monodromy group at infinity is affine equivalent to one of the chosen fields. In addition, quadratic vector fields with commutative monodromy group at infinity are described.     

Surface waves in electrostrictive materials under biasing fields

The theory of small incremental fields superposed on finite biasing fields in an electroelastic body is summarized first in this paper. The Stroh formalism for two-dimensional anisotropic elasticity and piezoelectricity is generalized to two-dimensional problems of an electroelastic body under biasing mechanical and electric fields. Application of this generalized Stroh formalism to study surface waves propagating in an electroelastic half-space under uniform initial fields indicates that there exist at most two surface waves even in the presence of biasing fields and these two surface waves correspond to the well-known Rayleigh and Bleustein waves in the mechanical nature. A simple procedure is established to distinguish these two types of waves. Application of the results to a model electrostrictive material is included for illustration. It is found that initial biasing fields can greatly influence propagation feature of surface waves.     

Halbordnungen und maximale Teilkörper in gelochten algebraisch-abgeschlossenen Körpern

In a former notice the author has shown that the so-calledh-closed fields (coming from halfordered fields) can be characterized in a similar way than the real closed fields (coming from ordered fields). But the case of characteristic 2 had been excluded. In this notice now a new characterization ofh-closed fields is given which includes fields of characteristic 2. Indeed, they are all maximal subfields of an algebraically closed field not containing a given element.     

On absolute Galois splitting fields of central simple algebras

A splitting field of a central simple algebra is said to be absolute Galois if it is Galois over some fixed subfield of the centre of the algebra. The paper proves an existence theorem for such fields over global fields with enough roots of unity. As an application, all twisted function fields and all twisted Laurent series rings over symbol algebras (or p-algebras) over global fields are crossed products. An analogous statement holds for division algebras over Henselian valued fields with global residue field.The existence of absolute Galois splitting fields in central simple algebras over global fields is equivalent to a suitable generalization of the weak Grunwald-Wang theorem, which is proved to hold if enough roots of unity are present. In general, it does not hold and counter examples have been used in noncrossed product constructions. This paper shows in particular that a certain computational difficulty involved in the construction of explicit examples of noncrossed product twisted Laurent series rings cannot be avoided by starting the construction with a symbol algebra.     

A note on powers in finite fields

The study of solutions to polynomial equations over finite fields has a long history in mathematics and is an interesting area of contemporary research. In recent years, the subject has found important applications in the modelling of problems from applied mathematical fields such as signal analysis, system theory, coding theory and cryptology. In this connection, it is of interest to know criteria for the existence of squares and other powers in arbitrary finite fields. Making good use of polynomial division in polynomial rings over finite fields, we have examined a classical criterion of Euler for squares in odd prime fields, giving it a formulation that is apt for generalization to arbitrary finite fields and powers. Our proof uses algebra rather than classical number theory, which makes it convenient when presenting basic methods of applied algebra in the classroom.     

循环数域导子的一点注记

主要研究循环数域的导子公式.利用Kronecker-Weber定理及整体域的分歧理论,对于给定除子分歧个数的素数次循环扩域,明确给出了这类数域的导子公式及其个数.     

Concircular vector fields on semi-Riemannian spaces

In this paper, we construct an analogue of concircular fields for semi-Riemannian spaces (i.e., for manifolds with degenerate metrics). We find a tensor criterion of spaces admitting the maximal number of concircular fields or having no such fields. We detect a gap in the distribution of dimensions of the space of concircular fields, which, in contrast to the corresponding gap in the case of pseudo-Riemannian manifolds, is lesser by 1. We also study some special types of concircular fields having no analogues for pseudo-Riemannian manifolds. The canonical form of the metric for some classes of semi-Riemannian spaces admitting concircular fields is obtained. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 31, Geometry, 2005.     

Hilbert Modular Threefolds of Arithmetic Genus One

In 1981, Weisser proved that there are exactly four Galois cubic number fields with Hilbert modular threefolds of arithmetic genus one. In this paper, we extend Weisser's work to cover all cubic number fields. Our main result is that there are exactly 33 fields with Hilbert modular threefolds of arithmetic genus one. These fields are enumerated explicitly.     

SU(2)规范场的恰当形式(欧空间)

应用数学机械化方法研究欧氏空间中SU(2)规范场的正规化问题.首先对Yang-Mills方程的表述进行了讨论,给出了一种具有物理和几何意义的YM-方程,称其为恰当的(exact)YM-方程.对于这种恰当的YM-方程,构造了一类线性微分变换,称之为SU(2)规范场的示性变换.经由示性变换,将非线性的恰当的YM-方程变为一组Laplace方程,实现了SU(2)规范场方程的线性化,即场方程的正规化.从而证明了SU(2)规范场存在3个独立的Yang-Mills规范场.     

On maximal immediate extensions of valued fields

We study the maximal immediate extensions of valued fields whose residue fields are perfect and whose value groups are divisible by the residue characteristic if it is positive. In the case where there is such an extension which has finite transcendence degree we derive strong properties of the field and the extension and show that the maximal immediate extension is unique up to isomorphism, although these fields need not be Kaplansky fields. If the maximal immediate extension is an algebraic extension, we show that it is equal to the perfect hull and the completion of the field.     

Quantum Fields as Pointlike Localized Objects,II

A class of quantum fields on a KREǐN space is considered. It is shown that these quantum fields are well defined objects at each space-time point in the meaning of sesquilinear forms. Conversely, it is proved that a special class of sesquilinear forms defines quantum fields on a KREǐN space.     

A random point field related to Bose-Einstein condensation

The random point fields which describe the position distributions of the systems of ideal boson gas in states of Bose-Einstein condensations are obtained through the thermodynamic limits. The resulting point fields are given by convolutions of two kinds of independent point fields: the so-called boson processes whose generating functionals are represented by the inverses of the Fredholm determinants for operators related to the heat operator and the point fields whose generating functionals are represented by the resolvents of the operators. The construction of the latter point fields in an abstract formulation is also given.     

Quantifier elimination for henselian fields relative to additive and multiplicative congruences

Several classes of henselian valued fields admit quantifier elimination relative to structures which reflect the additive and multiplicative congruences of the field. Value groups and residue fields may be viewed as reduts of these structures. A general theorem is given using the theory of tame extensions of henselian fields. Special cases like the case ofp-adically closed fields and the case of henselian fields of residue characteristic 0 are discussed. This work was completed during a visit in the Institute for Advanced Studies at the Hebrew University of Jerusalem.     

Conformal vector fields with respect to the Sasaki metric tensor

The purpose of this article is to characterize conformal vector fields with respect to the Sasaki metric tensor field on the tangent bundle of a Riemannian manifold of dimension at least three. In particular, if the manifold in question is compact, it is found that the only conformal vector fields are Killing vector fields.     

SU(3)规范场的恰当形式(欧空间)

应用数学机械化方法讨论SU(3)规范场的规范化问题.首先提出一种具有明确几何意义的Yang-Mills方程,称其为恰当的Yang-Mills方程.然后构造了一类线性微分变换,称之为SU(3)规范场的示性变换,它具体给出联络和截面之间的微分关系.经由示性变换,将非线性的恰当的YM-方程变为一组线性Laplace方程,即实现了规范场YM-方程的线性化.从而证明了SU(3)规范场包括8个独立的Yang-Mills规范场.