Dynamic multi-sector, multi-instrument financial networks with futures: Modeling and computation

In this paper, we develop a dynamic model of financial behavior in the case of multiple sectors and multiple instruments in the presence of financial futures, which demonstrates the evolution of the underlying networks through time. The dynamic model is formulated as a projected dynamical system whose set of stationary points coincides with the set of solutions to a variational inequality problem. We identify the network structure of the individual sectors' portfolio optimization problems out of equilibrium and then prove that the equilibrium solution can be reformulated as the solution to a network optimization problem, in which the network represents a merger of the individual networks. We subsequently provide a discrete time algorithm for the solution of the continuous time financial model, which exploits the network structure, and provide convergence results. The model and algorithm are then illustrated through numerical examples.