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2.
Signed graphs for portfolio analysis in risk management 总被引:1,自引:0,他引:1
Harary Frank; Lim Meng-Hiot; Wunsch Donald C. 《IMA Journal of Management Mathematics》2002,13(3):201-210
We introduce the notion of structural balance for signed graphsin the context of portfolio analysis. A portfolio of securitiescan be represented as a signed graph with the nodes denotingthe securities and the edges representing the correlation betweenthe securities. With signed graphs, the characteristics of aportfolio from a risk management perspective can be uncoveredfor analysis purposes. It is shown that a portfolio characterizedby a signed graph of positive and negative edges that is structurallybalanced is characteristically more predictable. Investors whoundertake a portfolio position with all positively correlatedsecurities do so with the intention to speculate on the upside(or downside). If the portfolio consists of negative edges andis balanced, then it is likely that the position has a hedgingdisposition within it. On the other hand, an unbalanced signedgraph is representative of an investment portfolio which ischaracteristically unpredictable. 相似文献
3.
M. A. Bertolim M. P. Mello K. A. de Rezende 《Transactions of the American Mathematical Society》2005,357(10):4091-4129
In this article the main theorem establishes the necessity and sufficiency of the Poincaré-Hopf inequalities in order for the Morse inequalities to hold. The convex hull of the collection of all Betti number vectors which satisfy the Morse inequalities for a pre-assigned index data determines a Morse polytope defined on the nonnegative orthant. Using results from network flow theory, a scheme is provided for constructing all possible Betti number vectors which satisfy the Morse inequalities for a pre-assigned index data. Geometrical properties of this polytope are described.
4.
Yao Ping HOU 《数学学报(英文版)》2005,21(4):955-960
A signed graph is a graph with a sign attached to each edge. This paper extends some fundamental concepts of the Laplacian matrices from graphs to signed graphs. In particular, the relationships between the least Laplacian eigenvalue and the unbalancedness of a signed graph are investigated. 相似文献
5.
Pingan Zeng Jiaquan Liu Yuxia Guo 《Journal of Mathematical Analysis and Applications》2004,300(1):102-128
In this paper, by using the Morse index theory for strongly indefinite functionals developed in [Nonlinear Anal. TMA, in press], we compute precisely the critical groups at the origin and at infinity, respectively. The abstract theorems are used to study the existence (multiplicity) of nontrivial periodical solutions for asymptotically wave equation and beam equation with resonance both at infinity and at zero. 相似文献
6.
Duan-zhi ZHANG School of Mathematical Sciences Peking University Beijing China 《中国科学A辑(英文版)》2007,50(6):761-772
In this paper, we study the Maslov-type index theory for linear Hamiltonian systems with brake orbits boundary value conditions and its applications to the existence of multiple brake orbits of nonlinear Hamiltonian systems. 相似文献
7.
For the NO molecule, modelled as a Morse oscillator, time-dependent (TD) nuclear Schr?dinger equation has been numerically
solved for the multiphoton vibrational dynamics of the molecule under a far-infrared laser of wavelength 10503 nm, and four
different intensities,I = 1 × 108, 1 × 1013, 5 × 1016, and 5 × 1018 W cm−2 respectively. Starting from the vibrational ground state at zero time, various TD quantities such as the norm, dissociation
probability, potential energy curve and dipole moment are examined. Rich high-harmonics generation (HHG) spectra and above-threshold
dissociation (ATD) spectra, due to the multiphoton interaction of vibrational motions with the laser field, and consequent
elevation to the vibrational continuum, have been obtained and analysed.
Dedicated to Professor C N R Rao on his 70th birthday
An erratum to this article is available at . 相似文献
8.
The set D of distinct signed degrees of the vertices in a signed graph G is called its signed degree set. In this paper, we prove that every non-empty set of positive (negative) integers is the
signed degree set of some connected signed graph and determine the smallest possible order for such a signed graph. We also
prove that every non-empty set of integers is the signed degree set of some connected signed graph. 相似文献
9.
Giuseppina Vannella 《Annali di Matematica Pura ed Applicata》2002,180(4):429-440
We consider a Neumann problem of the type -εΔu+F
′(u(x))=0 in an open bounded subset Ω of R
n
, where F is a real function which has exactly k maximum points.
Using Morse theory we find that, for ε suitably small, there are at least 2k nontrivial solutions of the problem and we give some qualitative information about them.
Received: October 30, 1999 Published online: December 19, 2001 相似文献
10.