fuzzy portfolio optimization under downside risk measures this paper presents two fuzzy portfolio selection models where the objective is to minimize the downside risk constrained by a given expected return we assume that the rates of returns on securities are approximated as lr fuzzy numbers of the same shape and that the expected return and risk are evaluated by interval valued means we establish the relationship between those mean interval definitions for a given fuzzy portfolio by using suitable ordering relations finally we formulate the portfolio selection problem as a linear program when the returns on the assets are of trapezoidal form

homotopy types of line arrangements we prove that the complement of a real affine line arrangement inc2 is homotopy equivalent to the canonical 2 complex associated with randell s presentation of the fundamental group this provides a much smaller model for the homotopy type of the complement of a real affine 2 or central 3 arrangement than the salvetti complex and its cousins as an application we prove that these exist infinitely many pairs of central arrangements inc3 with different underlying matroids whose complements are homotopy equivalent we also show that two real 3 arrangements whose oriented matroids are connected by a sequence of flips are homotopy equivalent

the ring structure on the cohomology of coordinate subspace arrangements every simplicial complex delta subset2 n on the vertex set n 1 ldots n defines a real resp complex arrangement of coordinate subspaces in mathbb r n resp mathbb c n via the correspondence delta ni sigma mapsto rm span e i i in sigma the linear structure of the cohomology of the complement of such an arrangement is explicitly given in terms of the combinatorics of delta and its links by the goresky macpherson formula here we derive by combinatorial means the ring structure on the integral cohomology in terms of data of delta we provide a non trivial example of different cohomology rings in the real and complex case furthermore we give an example of a coordinate arrangement that yields non trivial multiplication of torsion elements

on comparing interval numbers abstract this paper first presents a brief survey of the existing works on comparing and ranking any two interval numbers on the real line and then on the basis of this gives two approaches to compare any two interval numbers the first one describes a value judgement index along with a discussion on its strength and weakness over the other approaches this index has also been called an optimistic decision maker s preference index the other approach defines strict and fuzzy preference ordering between any two interval numbers from a pessimistic decision maker s point of view choice of different decision makers with different degrees of pessimism has also been considered

linear programming with fuzzy coefficients in constraints abstract this paper presents a new method for solving linear programming problems with fuzzy coefficients in constraints it is shown that such problems can be reduced to a linear semi infinite programming problem the relations between optimal solutions and extreme points of the linear semi infinite program are established a cutting plane algorithm is introduced with a convergence proof and a numerical example is included to illustrate the solution procedure

solving a class of fuzzy linear programs by using semi infinite programming techniques this paper deals with a class of fuzzy linear programming problems characterized by the fact that the coefficients in the constraints are modeled as lr fuzzy numbers with different shapes solving such problems is usually more complicated than finding a solution when all the fuzzy coefficients have the same shape we propose a primal semi infinite algorithm as a valuable tool for solving this class of fuzzy linear programs and we illustrate it by means of several examples

a possibilistic approach to selecting portfolios with highest utility score the mean variance methodology for the portfolio selection problem originally proposed by markowitz has been one of the most important research fields in modern finance in this paper we will assume that i each investor can assign a welfare or utility score to competing investment portfolios based on the expected return and risk of the portfolios and ii the rates of return on securities are modelled by possibility distributions rather than probability distributions we will present an algorithm of complexity o n3 for finding an exact optimal solution in the sense of utility scores to the n asset portfolio selection problem under possibility distributions

on the difference between real and complex arrangements if b is an arrangement of linear complex hyperplanes in c d then the following can be constructed from knowledge of its intersection lattice a the cohomology groups of the complement br b the cohomology algebra of the complement os c the fundamental group of the complement if d 2 d the singularity link up to homeomorphism if d 3 e the singularity link up to homotopy type zz if bis more generally a 2 arrangement in ir 2d an arrangement of real subspaces of codimension 2 with even dimensional intersections then the intersection lattice still determines a the cohomology groups of the complement gm and e the homotopy type of the singularity link zz we show however that for 2 arrangements the data b c and d are not deter mined by the intersection lattice they require the knowledge of extra information on sign patterns which can be computed as determinants of linear relations or equiva lently as linking coefficients in the sense of knot theory

portfolios with fuzzy returns selection strategies based on semi infinite programming this paper provides new models for portfolio selection in which the returns on securities are considered fuzzy numbers rather than random variables the investor s problem is to find the portfolio that minimizes the risk of achieving a return that is not less than the return of a riskless asset the corresponding optimal portfolio is derived using semi infinite programming in a soft framework the return on each asset and their membership functions are described using historical data the investment risk is approximated by mean intervals which evaluate the downside risk for a given fuzzy portfolio this approach is illustrated with a numerical example

fuzzy measures for profit maximization with fuzzy parameters profit maximization is an important issue to the firms that pursue the largest economic profit possible this paper extends the situation from the deterministic to uncertain where the coefficients are represented by fuzzy numbers intuitively when the problem has fuzzy parameters the derived profit value should be a fuzzy number as well the extension principle is utilized to develop a pair of two level mathematical programs to calculate the upper and lower bounds of the profit value at cuts following the duality theorem and a variable separation technique the two level mathematical programs are transformed into a class of one level signomial geometric programs to solve an example is given to illustrate the idea proposed in this paper

on the numerical treatment of linearly constrained semi infinite optimization problems abstract we consider the application of two primal algorithms to solve linear semi infinite programming problems depending on a real parameter combining a simplex type strategy with a feasible direction scheme we obtain a descent algorithm which enables us to manage the degeneracy of the extreme points efficiently the second algorithm runs a feasible direction method first and then switches to the purification procedure the linear programming subproblems that yield the search direction involve only a small subset of the constraints these subsets are updated at each iteration using a multi local optimization algorithm numerical test examples taken from the literature in order to compare the numerical effort with other methods show the efficiency of the proposed algorithms

hyperplane arrangement cohomology and monomials in the exterior algebra we show that if x is the complement of a complex hyperplane arrangement then the homology of x has linear free resolution as a module over the exterior algebra on the first cohomology of x we study invariants of x that can be deduced from this resolution a key ingredient is a result of aramova avramov and herzog 2000 on resolutions of monomial ideals in the exterior algebra we give a new conceptual proof of this result

fuzzy portfolio allocation models through a new risk measure and fuzzy sharpe ratio a new portfolio risk measure that is the uncertainty of portfolio fuzzy return is introduced in this paper beyond the well known sharpe ratio i e the reward to variability ratio in modern portfolio theory we initiate the so called fuzzy sharpe ratio in the fuzzy modeling context in addition to the introduction of the new risk measure we also put forward the reward to uncertainty ratio to assess the portfolio performance in fuzzy modeling corresponding to two approaches based on rm t rm m and rm t rm w fuzzy arithmetic two portfolio optimization models are formulated in which the uncertainty of portfolio fuzzy returns is minimized while the fuzzy sharpe ratio is maximized these models are solved by the fuzzy approach or by the genetic algorithm ga solutions of the two proposed models are shown to be dominant in terms of portfolio return uncertainty compared with those of the conventional mean variance optimization mvo model used prevalently in the financial literature in terms of portfolio performance evaluated by the fuzzy sharpe ratio and the reward to uncertainty ratio the model using rm t rm w fuzzy arithmetic results in higher performance portfolios than those obtained by both the mvo and the fuzzy model which employs rm t rm m fuzzy arithmetic we also find that using the fuzzy approach for solving multiobjective problems appears to achieve more optimal solutions than using ga although ga can offer a series of well diversified portfolio solutions diagrammed in a pareto frontier

outer automorphism groups of seifert 3 manifold groups over non orientable surfaces abstract in this paper we show that fundamental groups of seifert fibered spaces over non orientable surfaces have property e from this we deduce that the outer automorphism groups of almost all seifert groups are residually finite we conjecture that all outer automorphism groups of seifert groups are residually finite it follows that almost all mapping class groups of seifert fibered spaces are residually finite

on cohomology algebras of complex subspace arrangements the integer cohomology algebra of the complement of a complex subspace arrangement with geometric intersection lattice is completely determined by the combinatorial data of the arrangement we give a combinatorial presentation of the cohomology algebra in the spirit of the orlik solomon result on the cohomology algebras of complex hyperplane arrangements our methods are elementary we work with simplicial models for the complements that are induced by combinatorial stratifications of complex space we describe simplicial cochains that generate the cohomology among them we distinguish a linear basis study cup product multiplication and derive an algebra presentation in terms of generators and relations

class preserving automorphisms of certain hnn extensions abstract we show that for any integers class preserving automorphisms of the hnn extension b t t 1 h t h of a finitely generated nilpotent or free group b are all inner it follows from grossman s result that outer automorphism groups of such conjugacy separable hnn extensions are residually finite

perverse sheaves over real hyperplane arrangements let h be an arrangement of real hyperplanes in r the complexification of h defines a natural stratification of c we denote by perv c h the category of perverse sheaves on c smooth with respect to this stratification we give a description of perv c h as the category of representations of an explicit quiver with relations whose vertices correspond to real faces of h of all dimensions the relations are of monomial nature they identify some pairs of paths in the quiver they can be formulated in terms of the oriented matroid associated to h

nearest interval approximation of a fuzzy number the problem of the interval approximation of fuzzy numbers is discussed a new interval approximation operator which is the best one with respect to a certain measure of distance between fuzzy numbers is suggested

mean absolute deviation portfolio optimization model and its applications to tokyo stock market the purpose of this paper is to demonstrate that a portfolio optimization model using the l1 risk mean absolute deviation risk function can remove most of the difficulties associated with the classical markowitz s model while maintaining its advantages over equilibrium models in particular the l1 risk model leads to a linear program instead of a quadratic program so that a large scale optimization problem consisting of more than 1 000 stocks may be solved on a real time basis numerical experiments using the historical data of nikkei 225 stocks show that the l1 risk model generates a portfolio quite similar to that of the markowitz s model within a fraction of time required to solve the latter

combinatorial geometries convex polyhedra and schubert cells this paper is a continuation of gm which was published in the same journal we will explore a remarkable connection between the geometry of the schubert cells in the grassmann manifold the theory of convex polyhedra and the theory of combinatorial geometries in the sense of crapo and rota cr the results in this paper were obtained simultaneously and independently by gelfand and serganova in moscow and by goresky and macpherson at the i h e s in paris as part of larger programs with different purposes see below the geometry of this simple example is so beautiful that we decided to publish it independently of the applications we believe that combinatorial methods will play an increasing role in the future of geometry and topology we consider the grassmann manifold gi of all n k dimensional subspaces of c by fixing the standard basis in c we obtain an action of the torus h i on g pk which is induced from stretching the coordinate axes in c see also sect 1 we will describe not only the trajectories but also the strata of a new and interesting decomposition of the 301 oool 8708 87 7 50

class preserving automorphisms and inner automorphisms of certain tree products of groups abstract in general a class preserving automorphism of generalized free products of nilpotent groups need not be an inner automorphism we prove that every class preserving automorphism of tree products of finitely generated nilpotent or free groups amalgamating infinite cyclic subgroups is inner it follows that the outer automorphism groups of such tree products amalgamating infinite cyclic subgroups are residually finite

linear semi infinite programming theory an updated survey abstract this paper presents an state of the art survey on linear semi infinite programming theory and its extensions in particular convex semi infinite programming this review updates a previous survey semi infinite programming non convex optim appl 25 1998 of the same authors on the same topic which was published in 1998

on weighted possibilistic mean and variance of fuzzy numbers dubois and prade defined an interval valued expectation of fuzzy numbers viewing them as consonant random sets carlsson and fuller defined an interval valued mean value of fuzzy numbers viewing them as possibility distributions in this paper we shall introduce the notation of weighted interval valued possibilistic mean value of fuzzy numbers and investigate its relationship to the interval valued probabilistic mean we shall also introduce the notations of crisp weighted possibilistic mean value variance and covariance of fuzzy numbers which are consistent with the extension principle furthermore we show that the weighted variance of linear combination of fuzzy numbers can be computed in a similar manner as in probability theory

homotopy types of subspace arrangements via diagrams of spaces we prove combinatorial formulas for the homotopy type of the union of the subspaces in an affine compactified affine spherical or projective subspace arrangement from these formulas we derive results of goresky macpherson on the homology of the arrangement and the cohomology of its complement the union of an arrangement can be interpreted as the direct limit of a diagram of spaces over the intersection poset a closely related space is obtained by taking the homotopy direct limit of this diagram our method consists in constructing a combinatorial model diagram over the same poset whose homotopy limit can be compared to the original one by usual homotopy comparison results for diagrams of spaces

k parabolic subspace arrangements in this paper we study k parabolic arrangements a generalization of the k equal arrangement for any finite real reflection group when k 2 these arrangements correspond to the well studied coxeter arrangements brieskorn 1971 showed that the fundamental group of the complement of the type w coxeter arrangement over mathbb c is isomorphic to the pure artin group of type w khovanov 1996 gave an algebraic description for the fundamental group of the complement of the 3 equal arrangement over mathbb r we generalize khovanov s result to obtain an algebraic description of the fundamental group of the complement of the 3 parabolic arrangement for arbitrary finite reflection group our description is a real analogue to brieskorn s description

the cohomology rings of complements of subspace arrangements the ring structure of the integral cohomology of complements of real linear subspace arrangements is considered while the additive structure of the cohomology is given in terms of the intersection poset and dimension function by a theorem of goresky and macpherson we describe the multiplicative structure in terms of the intersection poset the dimension function and orientations of the participating subspaces for the class of arrangements without pairs of intersections of codimension one in particular this yields a description of the integral cohomology ring of complex arrangements conjectured by yuzvinsky for general real arrangements a weaker result is obtained the approach is geometric and the methods are elementary

convexity properties of the moment mapping ii be its associated momen t mapping see w for definitions the set x is the union of co adjoint orbits the main result of this paper is a description of the orbit structure of this set to describe this result we first note that the coadjoint orbits in q can be parametr ized as follows let t be a caf tan subalgebra of g and let b be a positive definite g invariant bilinear form on by means of b we get a g equivariant identification q let t be the subspace of q corresponding to t then every co adjoint orbit intersects i in a weyl group orbit so there is a one one correspondence between co adjoint orbits in q and weyl group orbits in t to get an even sharper parametrization let t be a weyl chamber in then every weyl group orbit intersects t in a single point so t is a modul i space for the co adjoint orbits two orbits in x are said to be of the same type if they are isomorphic as homogeneous g spaces since x is compact there are at most a finite number of different types of orbits see 1113 let h be a closed subgroup of t of codimension r and let cit be the set of all orbits in x of type g h

the mean value of a fuzzy number abstract the notion of expectation is defined for fuzzy numbers of intervals viewing them as consonant random sets this expectation is interval valued and remains additive in the sense of fuzzy interval addition as a by product some light is shed on the debate between probability and possibility theory and the problem of how to carry measure theoretic notions into the field of possibility theory

higher homotopy groups of complements of complex hyperplane arrangements abstract we generalize results of hattori on the topology of complements of hyperplane arrangements from the class of generic arrangements to the much broader class of hypersolvable arrangements we show that the higher homotopy groups of the complement vanish in a certain combinatorially determined range and we give an explicit z 1 module presentation of p the first non vanishing higher homotopy group we also give a combinatorial formula for the 1 coinvariants of p for affine line arrangements whose cones are hypersolvable we provide a minimal resolution of 2 and study some of the properties of this module for graphic arrangements associated to graphs with no 3 cycles the algorithm for computing 2 is purely combinatorial the fitting varieties associated to 2 may distinguish the homotopy 2 types of arrangement complements with the same 1 and the same betti numbers in low degrees

a multi objective genetic algorithm for cardinality constrained fuzzy portfolio selection this paper presents a new procedure that extends genetic algorithms from their traditional domain of optimization to fuzzy ranking strategy for selecting efficient portfolios of restricted cardinality the uncertainty of the returns on a given portfolio is modeled using fuzzy quantities and a downside risk function is used to describe the investor s aversion to risk the fitness functions are based both on the value and the ambiguity of the trapezoidal fuzzy number which represents the uncertainty on the return the soft computing approach allows us to consider uncertainty and vagueness in databases and also to incorporate subjective characteristics into the portfolio selection problem we use a data set from the spanish stock market to illustrate the performance of our approach to the portfolio selection problem

fuzzy and semi infinite mathematical programming abstract in this paper linkups between imprecision and infinity in an optimization framework are highlighted inspired by these connections the new potential opened up by semi infinite optimization is gainfully exploited to push forward an approach for solving a fuzzy mathematical program issues regarding the viability of the approach as well as the satisfying character of solutions yielded by this way are also addressed furthermore we present a cutting plane method for solving the resulting semi infinite program we end up by some concluding remarks and indicate directions for further developments

portfolio selection under independent possibilistic information this paper deals with a portfolio selection problem with independently estimated possibilistic return rates under such a circumstance a distributive investment has been regarded as a good solution in the traditional portfolio theory however the conventional possibilistic approach yields a concentrated investment solution considering the reason why a distributive investment is advocated a new approach to the possibilistic portfolio selection is proposed

combinatorial stratification of complex arrangements we present a method for discretizing complex hyperplane arrange ments by encoding their topology into a finite partially ordered set of sign vectors this is used in the following ways 1 a general method is given for constructing regular cell complexes having the homotopy type of the complement of the arrangement 2 for the case of complexified arrangements this specializes to the con struction of salvetti s we study the combinatorial structure of complexified arrangements and the salvetti complex in some detail 3 this general method simultaneously produces cell decompositions of the singularity link this link is shown to have the homotopy type of a wedge of d spheres for arrangements in cd d 4 4 the homology of the link and the cohomology of the complement are computed in terms of explicit bases which are matched by alexander duality this gives a new more elementary and more generally valid proof for the brieskorn orlik solomon theorem and some related results 5 our setup leads to a more general notion of 2 pseudoarrangements which can be thought of as topologically deformed complex arrangements re taining only the essential topological and combinatorial structure we show that all of the above remains true in this generality except for the sign patterns of the orlik solomon relations department of mathematics royal institute of technology s10044 stockholm sweden e mail address andersb nada kth se institut fur mathematik universitat augsburg d 8900 augsburg germany current address institut mittag leffler auravagen 17 s 18262 djursholm sweden address after 1 april 1992 konrad zuse zentrum fur informationstechnik berlin heilbronner str 10 w 1000 berlin 31 germany e mail addresses ziegler ml kva se ziegler zib berlin de this content downloaded from 157 55 39 211 on fri 24 jun 2016 06 44 45 utc all use subject to http about jstor org terms