Juntao Wang
ABSTRACT
Directed network with flow dynamics is an important topic in realistic complex systems such as banking systems. We study the stability of these financial networks using a homogeneous and a more general inhomogeneous model. The nodes of the networks are banks and they are under four different kinds of disturbance that may lead to bankruptcy, which is defined by the condition that the capital value of the bank is below a critical value, such as zero. The stability of this network is measured by the minimum value of capital of the nodes after a fixed time of money flow in the network. The smaller the minimum value, the higher the probability of the first bankruptcy. By means of genetic algorithm with networks as the chromosome, the edges between nodes as genes, we can perform evolutionary computation using rewiring of edges as the genetic operators to search for a network topology with high stability. Our analytical results on flow dynamics are based on the linear relation between net change and PageRank centrality under small damping factor. Our numerical analysis shows that genetic algorithm can be very efficient in finding network with given connectivity that is stable against four categories of disturbance, namely under internal (and external) perturbation that is cumulative or noncumulative. Our results show that a banking network with each bank with similar relative wealth (thus small Gini coefficient in wealth distribution) is more stable than one with highly unequal wealth distribution. We also find our optimization method works for delaying the second bankruptcy after the first. These results may be useful in practical applications for the prevention of the first failure, as well as cascade failures in real complex systems.
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Index Terms
- Optimization of financial network stability by genetic algorithm
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