Financial networks with electronic transactions: modelling, analysis and computations

Advances in telecommunication networks, and, in particular, the Internet have transformed the economic landscape for financial decision-making. In this paper, we focus on financial networks with electronic transactions and with different tiers of decision-makers and we develop an integrated framework for the modelling, analysis and computation of solutions to such problems. Specifically, we consider an economy consisting of three types of decision-makers: those with sources of funds; intermediary ones, and consumers associated with the financial products at the demand markets. Those with sources of funds can transact with the intermediaries either physically or electronically as well as directly in an electronic manner with the consumers. The intermediaries, in turn, can also transact with the consumers either in a physical or an electronic fashion. We address the behaviour of the decision-makers, identify the network structure of the problem, derive the equilibrium conditions, and establish the variational inequality formulation. In addition, we propose a continuous time adjustment process for the study of the disequilibrium dynamics and prove that the set of stationary points of the resulting projected dynamical system coincides with the set of solutions of the variational inequality. We then utilize variational inequality theory to derive qualitative properties of the equilibrium price and financial flow pattern. Finally, we apply an algorithm for the determination of equilibrium prices and financial flows in several examples.