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Markovian Nash equilibrium in financial markets with asymmetric information and related forward-backward systems

Çetin, Umut and Danilova, Albina (2016) Markovian Nash equilibrium in financial markets with asymmetric information and related forward-backward systems. Annals of Applied Probability, 26 (4). pp. 1996-2029. ISSN 1050-5164

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Identification Number: 10.1214/15-AAP1138

Abstract

This paper develops a new methodology for studying continuous-time Nash equilibrium in a financial market with asymmetrically informed agents. This approach allows us to lift the restriction of risk neutrality imposed on market makers by the current literature. It turns out that, when the market makers are risk averse, the optimal strategies of the agents are solutions of a forward- backward system of partial and stochastic differential equations. In particular, the price set by the market makers solves a non-standard `quadratic' backward stochastic differential equation. The main result of the paper is the existence of a Markovian solution to this forward-backward system on an arbitrary time interval, which is obtained via a fixed-point argument on the space of absolutely continuous distribution functions. Moreover, the equilibrium obtained in this paper is able to explain several stylized facts which are not captured by the current asymmetric information models.

Item Type: Article
Official URL: http://www.imstat.org/aap/
Additional Information: © 2016 Institute of Mathematical Statistics
Divisions: Mathematics
Statistics
Subjects: H Social Sciences > HG Finance
Q Science > QA Mathematics
Sets: Departments > Mathematics
Departments > Statistics
Date Deposited: 19 Aug 2015 09:02
Last Modified: 20 Mar 2019 02:51
URI: http://eprints.lse.ac.uk/id/eprint/63259

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