Liquidity induced asset bubbles via flows of ELMMs

Abstract

We consider a constructive model for asset price bubbles, where the market price $W$ is endogenously determined by the trading activity on the market and the fundamental price $W^F$ is exogenously given, as in [R. Jarrow, P. Protter, and A. Roch, Quant. Finance, 12 (2012), pp. 1339--1349]. To justify $W^F$ from a fundamental point of view, we embed this constructive approach in the martingale theory of bubbles (see [R. Jarrow, P. Protter, and K. Shimbo, Math. Finance, 20 (2010), pp. 145--185] and [F. Biagini, H. Föllmer, and S. Nedelcu, Finance Stoch., 18 (2014), pp. 297--326]) by showing the existence of a flow of equivalent martingale measures for $W$, under which $W^F$ equals the expectation of the discounted future cash flow. As an application, we study bubble formation and evolution in a financial network.