Related papers: Dynamic asset trees and Black Monday
Understanding the response of an output variable to multi-dimensional inputs lies at the heart of many data exploration endeavours. Topology-based methods, in particular Morse theory and persistent homology, provide a useful framework for…
The global structure of the minimal spanning tree (MST) is expected to be universal for a large class of underlying random discrete structures. However, very little is known about the intrinsic geometry of MSTs of most standard models, and…
Diversification of an investment into independently fluctuating assets reduces its risk. In reality, movement of assets are are mutually correlated and therefore knowledge of cross--correlations among asset price movements are of great…
The waiting time needed for a stock market index to undergo a given percentage change in its value is found to have an up-down asymmetry, which, surprisingly, is not observed for the individual stocks composing that index. To explain this,…
We show that the limit in our definition of tree shift topological entropy is actually the infimum, as is the case for both the topological and measure-theoretic entropies in the classical situation when the time parameter is $\mathbb Z$.…
The connectivity of stock markets reflects the information efficiency of capital markets and contributes to interior risk contagion and spillover effects. We compare Shanghai Stock Exchange A-shares (SSE A-shares) during tranquil periods,…
A behavior of extreme networks under deformations of their boundary sets is investigated. It is shown that analyticity of a deformation of boundary set guarantees preservation of the networks types for minimal spanning trees, minimal…
We introduce a discrete binary tree for pricing contingent claims with the underlying security prices exhibiting history dependence characteristic of that induced by market microstructure phenomena. Example dependencies considered include…
We propose a data-driven Neural Network (NN) optimization framework to determine the optimal multi-period dynamic asset allocation strategy for outperforming a general stochastic target. We formulate the problem as an optimal stochastic…
We consider the minimum spanning tree problem in a setting where information about the edge weights of the given graph is uncertain. Initially, for each edge $e$ of the graph only a set $A_e$, called an uncertainty area, that contains the…
We empirically investigated the effects of market factors on the information flow created from N(N-1)/2 linkage relationships among stocks. We also examined the possibility of employing the minimal spanning tree (MST) method, which is…
We study trade-based manipulation of stock prices from the perspective of complex trading networks constructed by using detailed information of trades. A stock trading network consists of nodes and directed links, where every trader is a…
Motivated by an application in computational topology, we consider a novel variant of the problem of efficiently maintaining dynamic rooted trees. This variant requires merging two paths in a single operation. In contrast to the standard…
We study a new type of random minimum spanning trees. It is built on the complete graph where each vertex is given a weight, which is a positive real number. Then, each edge is given a capacity which is a random variable that only depends…
Complex systems comprise a large number of interacting elements, whose dynamics is not always a priori known. In these cases -- in order to uncover their key features -- we have to turn to empirical methods, one of which was recently…
This paper presents a non-minimal order dynamics model for many analysis, simulation, and control problems of constrained mechanical systems with switching topology by making use of linear projection operator. The distinct features of this…
We investigate the emergence of a structure in the correlation matrix of assets' returns as the time-horizon over which returns are computed increases from the minutes to the daily scale. We analyze data from different stock markets (New…
This paper is aimed to investigate some computational aspects of different isoperimetric problems on weighted trees. In this regard, we consider different connectivity parameters called {\it minimum normalized cuts}/{\it isoperimteric…
Evidence is offered for log-periodic (in time) fluctuations in the S&P 500 stock index during the three years prior to the October 27, 1997 "correction". These fluctuations were expected on the basis of a discretely scale invariant rupture…
Geometry-inspired measures (such as discrete Ricci curvatures) and topological data analysis (TDA) based methods (such as persistent homology) have become attractive tools for characterizing the higher-order structure of networks…