Economic Equilibrium with Random Transactions

This paper presents the advances in modelling the system of agents under the conditions of random transactions between them. We face certain challenges in this project which we would like to highlight in this presentation. The agents in the modelled system are a large number of consumers, a large number of producers and the bank as the intermediary. Consumers take loans from the bank to spend on consumption goods and producers borrow to make investment at random moments of time. The moments of time the agents deal form the Poisson flow. We present the approach to agents' optimal control problems by the Lagrange method instead of dynamic programming. This enables us obtaining the expressions for the optimal feedback control which appear to be linear in state variables. The solution to the optimal control problems are obtained using asymptotic methods assuming large frequency of transactions. Using the linearity of the agents' optimal control, we may aggregate description of agents, stock-flow consistent on the average. Instead of an ensemble of independent random transactions by agents, the description of the aggregate dynamics is deterministic. The system of equations for the aggregate dynamics is reduced to one equation. There are two cases of this equation, depending on the description of the bank. The equation has a specific form, its numerical analysis is challenging. We provide numerical results and discuss further directions of research.