2017/09/30 by Borovykh, Anastasia, Pascucci, Andrea, la Rovere, Stefano
#97M30 #FOS: Economics and business #Mathematical Finance (q-fin.MF)
paper · doi:10.48550/arxiv.1710.00231
In this paper we consider a mean-field model of interacting diffusions for the monetary reserves in which the reserves are subjected to a self- and cross-exciting shock. This is motivated by the financial acceleration and fire sales observed in the market. We derive a mean-field limit using a weak convergence analysis and find an explicit measure-valued process associated with a large interbanking system. We define systemic risk indicators and derive, using the limiting process, several law of large numbers results and verify these numerically. We conclude that self-exciting shocks increase the systemic risk in the network and their presence in interbank networks should not be ignored.