Liquidity induced asset bubbles via flows of ELMMs

TL;DR

This paper develops a model for asset price bubbles where market prices are driven by trading activity and fundamental prices are externally given, integrating the martingale theory of bubbles to justify fundamental values.

Contribution

It introduces a constructive framework linking endogenous market prices with exogenous fundamentals using flows of equivalent martingale measures.

Findings

Existence of a flow of EMMs for the market price process.

Demonstration of fundamental price justification within the martingale framework.

Application to bubble formation and evolution in financial networks.

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 the work of Jarrow, Protter and Roch (2012). To justify $W^F$ from a fundamental point of view, we embed this constructive approach in the martingale theory of bubbles, see Jarrow, Protter and Shimbo (2010) and Biagini, F\"ollmer and Nedelcu (2014), 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.