Optimal Bubble Riding with Price-dependent Entry: a Mean Field Game of Controls with Common Noise

TL;DR

This paper extends a bubble riding model by incorporating price-dependent entry times, leading to a mean field game with common noise, and provides an existence proof for the equilibrium in this complex setting.

Contribution

It introduces a novel mean field game framework with random entry and common noise, extending previous bubble models and establishing existence results.

Findings

Existence of equilibrium in the extended model.

Incorporation of price-dependent entry into mean field game.

Analysis of common noise effects on bubble dynamics.

Abstract

In this paper we further extend the optimal bubble riding model proposed by Tangpi and Wang by allowing for price-dependent entry times. Agents are characterized by their individual entry threshold that represents their belief in the strength of the bubble. Conversely, the growth dynamics of the bubble is fueled by the influx of players. Price-dependent entry naturally leads to a mean field game of controls with common noise and random entry time, for which we provide an existence result. The equilibrium is obtained by first solving discretized versions of the game in the weak formulation and then examining the measurability property in the limit. In this paper, the common noise comes from two sources: the price of the asset which all agents trade, and also the exogenous bubble burst time, which we also discretize and incorporate into the model via progressive enlargement of filtration.