Advantages Of Graph Theory Research Articles

New criteria of almost sure exponential stability and instability of nonlinear stochastic systems with a generalization to stochastic coupled systems

This paper focuses on the almost sure exponential stability and instability problems for nonlinear stochastic systems. In contrast with previous works, combining with Lyapunov’s second method and inequalities techniques, two classes of less conservative criteria are obtained, depending on piecewise continuous scalar functions (PCSFs). It is highly desirable that the PCSF can not only replace the constant coefficient of the upper bound estimation which belongs to the diffusion operator of a Lyapunov function in available literature but also even be unbounded. Especially, when PCSFs are assumed to be periodic, our theoretical results can be transformed into the case of almost sure exponential stability and instability of nonlinear systems with intermittent noises, and corresponding criteria are derived. Furthermore, the sufficient criteria we present are popularized to stochastic coupled systems taking advantage of graph theory and Lyapunov method. As an application of theoretical results, we put forward an exploration to the synchronization analysis of a class of single-link robot arms system via intermittent noise control. Finally, several numerical examples consisting of a time-varying stochastic system and a stochastic coupled oscillators system as well as single-link robot arms systems are provided to illustrate the feasibility of the stated theoretical results.

The Bond–Equity–Fund Relation Using the Fama–French–Carhart Factors: A Practical Network Approach

The main goal of this article is to show the relation between global equity and bond funds from a network perspective. The authors demonstrate the advantages of graph theory to explain the collective fund dynamics. The results show that equity and bond funds have a significant exposure to the Fama–French–Carhart factors. The authors argue that the network is dynamically driven by equity funds with their centrality scores and risk factor exposure and can transmit and amplify system-wide stress or inefficiencies in the factor bets. Using graph theory, the authors demonstrate that the return-based relationships between bond and equity funds are asymmetrical and the network is sufficiently clustered. Specifically, equity funds connect the different clusters. The HML factor is significant both on a single-fund level and as a web determinant. Therefore, investors should pay close attention to it when managing funds and deriving asset allocations. Finally, the authors provide a machine learning approach to how fund managers, plan sponsors, and analysts can derive equity–bond allocations, based on centrality scores, factor exposure, and hierarchical clustering of asymmetrically connected assets. TOPICS:Equity portfolio management, statistical methods, simulations, big data/machine learning Key Findings • The authors use topology and a concept from physics to show strong–weak return- and factor-based relationships between global equity and bond funds using a directed network approach. • The Fama–French–Carhart factors determine an asymmetrical bond–equity fund relation and different fund clusters. The network exhibits a structure that differs according to the market cycle. Equity funds play the most central role in the market and connect the different clusters. • Investors can use the bond–equity interconnectedness and network topology in multiple ways. The authors show that simple passive allocations, fund-of-funds solutions, and cluster-wise control for risk factors are some of the possible applications.