Liquidity Based Modeling of Asset Price Bubbles via Random Matching

In this paper we study the evolution of asset price bubbles driven by contagion effects spreadingamong investors via a random matching mechanism in a discrete-time version of the liquidity basedmodel of [R. A. Jarrow, P. Protter, and A. F. Roch,Quant. Finance, 12 (2012), pp. 1339--1349].To this scope, we extend the Markov conditionally independent dynamic directed random matchingof [D. Duffie, L. Qiao, and Y. Sun,J. Econ. Theory, 174 (2018), pp. 124--183] to a stochasticsetting to include stochastic exogenous factors in the model. We derive conditions guaranteeing thatthe financial market model is arbitrage-free and present some numerical simulation illustrating ourapproach.