q-fin updates on arXiv.org
Tue, 03 Mar 2020 12:02:32 GMT language
We consider a random financial network with a large number of agents. The
agents connect through credit instruments borrowed from each other or through
direct lending, and these create the liabilities. The settlement of the debts
of various agents at the end of the contract period can be expressed as
solutions of random fixed point equations. Our first step is to derive these
solutions (asymptotically), using a recent result on random fixed point
equations. We consider a large population in which agents adapt one of the two
available strategies, risky or risk-free investments, with an aim to maximize
their expected returns (or surplus). We aim to study the emerging strategies
when different types of replicator dynamics capture inter-agent interactions.
We theoretically reduced the analysis of the complex system to that of an
appropriate ordinary differential equation (ODE). We proved that the
equilibrium strategies converge almost surely to that of an attractor of the
ODE. We also derived the conditions under which a mixed evolutionary stable
strategy (ESS) emerges; in these scenarios the replicator dynamics converges to
an equilibrium at which the expected returns of both the populations are equal.
Further the average dynamics (choices based on large observation sample) always
averts systemic risk events (events with large fraction of defaults). We
verified through Monte Carlo simulations that the equilibrium suggested by the
ODE method indeed represents the limit of the dynamics.