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

Umut Çetin and Albina Danilova

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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.

Keywords: Kyle model with risk averse market makers; Bertrand competition; forward–backward stochastic and partial differential equations; Markov bridges (search for similar items in EconPapers)
JEL-codes: F3 G3 (search for similar items in EconPapers)
Date: 2016-08-01
New Economics Papers: this item is included in nep-ore
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Citations: View citations in EconPapers (14)

Published in Annals of Applied Probability, 1, August, 2016, 26(4), pp. 1996-2029. ISSN: 1050-5164

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