Price dynamics on a risk-averse market with asymmetric information

TL;DR

This paper extends the analysis of price dynamics in markets with asymmetric information to risk-averse agents, showing that prices still follow a CMMV process under a martingale measure, thus supporting its use in financial modeling.

Contribution

It demonstrates that even with risk-averse agents, the price process remains a CMMV, generalizing previous results from risk-neutral settings.

Findings

Price process is a CMMV under a martingale measure with risk-averse agents.

Theoretical justification for using CMMV dynamics in risk-averse markets.

Includes Black-Scholes model as a special case.

Abstract

A market with asymmetric information can be viewed as a repeated exchange game between the informed sector and the uninformed one. In a market with risk-neutral agents, De Meyer [2010] proves that the price process should be a particular kind of Brownian martingale called CMMV. This type of dynamics is due to the strategic use of their private information by the informed agents. In the current paper, we consider the more realistic case where agents on the market are risk-averse. This case is much more complex to analyze as it leads to a non-zero-sum game. Our main result is that the price process is still a CMMV under a martingale equivalent measure. This paper provides thus a theoretical justification for the use of the CMMV class of dynamics in financial analysis. This class contains as a particular case the Black and Scholes dynamics.