Liquidity generated by heterogeneous beliefs and costly estimations

Min Shen; Gabriel Turinici

doi:10.3934/nhm.2012.7.349

Article Contents

2012, Volume 7, Issue 2: 349-361. Doi: 10.3934/nhm.2012.7.349 open access

This issue Previous Article A modest proposal for MFG with density constraints Next Article

Liquidity generated by heterogeneous beliefs and costly estimations

Min Shen^1, and
Gabriel Turinici^2,

1.
CEREMADE, Universite Paris Dauphine, Place du Marechal de Lattre de Tassigny, 75016 Paris
2.
CEREMADE, Université Paris Dauphine, Place du Marechal de Lattre de Tassigny, 75016 Paris

Received: October 31, 2011

Revised: February 29, 2012

Published: May 2012

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Abstract

We study the liquidity, defined as the size of the trading volume, in a situation where an infinite number of agents with heterogeneous beliefs reach a trade-off between the cost of a precise estimation (variable depending on the agent) and the expected wealth from trading. The "true" asset price is not known and the market price is set at a level that clears the market. We show that, under some technical assumptions, the model has natural properties such as monotony of supply and demand functions with respect to the price, existence of an equilibrium and monotony with respect to the marginal cost of information. We also situate our approach within the Mean Field Games (MFG) framework of Lions and Lasry which allows to obtain an interpretation as a limit of Nash equilibrium for an infinite number of agents.

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Mathematics Subject Classification: Primary: 91B24, 91B26; Secondary: 91Gxx.

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