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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.
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
4.
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
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A (p, q)-sigraph S is an ordered pair (G, s) where G = (V, E) is a (p, q)-graph and s is a function which assigns to each edge of G a positive or a negative sign. Let the sets E
+ and E
– consist of m positive and n negative edges of G, respectively, where m + n = q. Given positive integers k and d, S is said to be (k, d)-graceful if the vertices of G can be labeled with distinct integers from the set {0, 1, ..., k + (q – 1)d such that when each edge uv of G is assigned the product of its sign and the absolute difference of the integers assigned to u and v the edges in E
+ and E
– are labeled k, k + d, k + 2d, ..., k + (m – 1)d and –k, – (k + d), – (k + 2d), ..., – (k + (n – 1)d), respectively.In this paper, we report results of our preliminary investigation on the above new notion, which indeed generalises the well-known concept of (k, d)-graceful graphs due to B. D. Acharya and S. M. Hegde. 相似文献
7.
Palle E.T. Jorgensen Erin P.J. Pearse 《Journal of Mathematical Analysis and Applications》2019,469(2):765-807
Motivated by applications to machine learning, we construct a reversible and irreducible Markov chain whose state space is a certain collection of measurable sets of a chosen l.c.h. space . We study the resulting network (connected undirected graph), including transience, Royden and Riesz decompositions, and kernel factorization. We describe a construction for Hilbert spaces of signed measures which comes equipped with a new notion of reproducing kernels and there is a unique solution to a regularized optimization problem involving the approximation of functions by functions of finite energy. The latter has applications to machine learning (for Markov random fields, for example). 相似文献
8.
本文首先引入Fuzzy集类上(广义)可加Fuzzy测度的有关概念,然后给出Fuzzy集上关于可加Fuzzy测度的Fuaay积分及有关定理,最后在一定条件下给出广义可加Fuzzy测度的一系列分解定理。 相似文献
9.
The Maximum Balanced Subgraph Problem (MBSP) is the problem of finding a subgraph of a signed graph that is balanced and maximizes the cardinality of its vertex set. This paper is the first one to discuss applications of the MBSP arising in three different research areas: the detection of embedded structures, portfolio analysis in risk management and community structure. The efficient solution of the MBSP is also in the focus of this paper. We discuss pre-processing routines and heuristic solution approaches to the problem. a GRASP metaheuristic is developed and improved versions of a greedy heuristic are discussed. Extensive computational experiments are carried out on a set of instances from the applications previously mentioned as well as on a set of random instances. 相似文献
10.