Physics (Internal)

Dissipative Dynamics in Financial Networks

This event is part of the Preliminary Oral Exam.

Examining Committee: Professors Gene Stanley, Irena Vodenska, Tulika Bose, William Skocpol

Abstract:

We have devised a model for the dynamics of bipartite network of banks vs assets near equilibrium which suggests that the dynamics of this system can be mapped to a dissipative dynamical system. In particular we identify the criteria under which the network would be a closed system and non-dissipative by finding the Lagrangian terms that yield the proposed dynamical equations. As in principle there can be many other players in the actual network of which we do not have precise knowledge (i.e. the known network could be part of a bigger system) we modify the Lagragian dynamics by adding dissipation to it. The dissipative terms assume a mean field value for the effects of the unknown parts of the network. We also argue that to lowest order, our model is close to the most general model that can be written down for such a system. Another goal of this work was to assess the systemic importance of the banks in the network. We argue that because our network is highly dynamic a dynamic measure of centrality is needed. We define one such measure, which we refer to as BankRank, related to the rate of loss of money in the system due to failure of each bank. We use the Pearson correlation of BankRank with asset values as an order parameter and find that the model has a rich phase diagram with a few phase transitions. As a side, we also find that there are many metastable regions which are separated by sharp walls. The walls are related to communities. and each community has almost the same value of BankRank.