The Annals of Applied Probability

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

Umut Çetin and Albina Danilova

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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 nonstandard “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.

Article information

Ann. Appl. Probab., Volume 26, Number 4 (2016), 1996-2029.

Received: August 2014
Revised: July 2015
First available in Project Euclid: 1 September 2016

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Zentralblatt MATH identifier

Primary: 60H30: Applications of stochastic analysis (to PDE, etc.) 60J60: Diffusion processes [See also 58J65]
Secondary: 91B44: Informational economics

Kyle model with risk averse market makers Bertrand competition forward–backward stochastic and partial differential equations Markov bridges


Çetin, Umut; Danilova, Albina. Markovian Nash equilibrium in financial markets with asymmetric information and related forward–backward systems. Ann. Appl. Probab. 26 (2016), no. 4, 1996--2029. doi:10.1214/15-AAP1138.

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