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August 2016 Markovian Nash equilibrium in financial markets with asymmetric information and related forward–backward systems
Umut Çetin, Albina Danilova
Ann. Appl. Probab. 26(4): 1996-2029 (August 2016). DOI: 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 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.

Citation

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Umut Çetin. Albina Danilova. "Markovian Nash equilibrium in financial markets with asymmetric information and related forward–backward systems." Ann. Appl. Probab. 26 (4) 1996 - 2029, August 2016. https://doi.org/10.1214/15-AAP1138

Information

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

zbMATH: 1353.91050
MathSciNet: MR3543888
Digital Object Identifier: 10.1214/15-AAP1138

Subjects:
Primary: 60H30 , 60J60
Secondary: 91B44

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

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.26 • No. 4 • August 2016
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