A PÓLYA LATTICE MODEL TO STUDY LEVERAGE DYNAMICS AND CONTAGIOUS FINANCIAL FRAGILITY

Abstract

We discuss a special Pólya lattice model to study cascading failures of firms in a simple industrial economy. In particular, every firm is represented by a Pólya-like urn, whose reinforcement is function of time, of the neighboring urns and their compositions, and of a random variable representing systemic risk or fate. The simple idea is to build the dependence among firms by assuming simple balance sheet rules on debts and credits. In detail we assume that the debts of every company are credits for some of its neighbors. Debts and credits are represented by different balls in the urns/firms. At the same time we assume that the riskiness of every firm also depends on the economic wealth of its neighbors and of the economy in general. These simple rules are sufficient to create business cycles, in which the accumulation of debts pushes the economy towards frequent crises. The model can be easily simulated and the results we obtain encourage the development of brand new finitary probabilistic approaches to study firms' behavior and dynamics.