Advances in Complex Systems

In order to unveil the value of network connectivity, discounted both in space and time, we formalize the construction of networks as an optimal control dynamic graph-theoretic problem. The network is based on a set of leaders and followers linked through edges. The node dynamics, built upon the consensus protocol, form a time evolutive Mahalanobis distance weighted by the opportunity costs. The results show that the network equilibrium depends on the influence of leader nodes, while the network connectivity depends on the cohesiveness among followers. Through numerical simulations, we find that — past a threshold level of opportunity costs — the values of shadow prices become stationary. Likewise, the model outputs show that, at a fixed level of foregone gains, agents value the safeguard of connections less in time than in space.

We introduce a method to infer lead-lag networks of agents’ actions in complex systems. These networks open the way to both microscopic and macroscopic states prediction in such systems. We apply this method to trader-resolved data in the foreign exchange market. We show that these networks are remarkably persistent, which explains why and how order flow prediction is possible from trader-resolved data. In addition, if traders’ actions depend on past prices, the evolution of the average price paid by traders may also be predictable. Using random forests, we verify that the predictability of both the sign of order flow and the direction of average transaction price is strong for retail investors at an hourly time scale, which is of great relevance to brokers and order matching engines. Finally, we argue that the existence of trader lead-lag networks explains in a self-referential way why a given trader becomes active, which is in line with the fact that most trading activity has an endogenous origin.

This paper establishes a trade credit network with a guarantee mechanism. Based on the established network model, the trade credit network and the guarantee network are visualized. The characteristics of the distributions of both networks and the firm size distribution are then researched. Concurrently, through computer simulations, the risk contagion among firms is analyzed on the basis of the interactions between the trade credit network and the guarantee network. The results are as follows: (1) the degree of the trade credit network takes on a power-law distribution, as does the upper tail of firm size. (2) For the degree distribution of the guarantee network, the test result of the power-law features changes with a varying value of $\varpi$ based on the test method of Clauset, [Shalizi and Newman Power-law distributions in empirical data, SIAM Rev. 51 (2009) 661–703]. The change in $\varpi$ directly affects the establishment of the guarantee links, thus affecting the structure of the guarantee network and its power-law features. (3) Finally, the introduction of a guarantee mechanism aggravates the extent of the risk contagion among firms.