Abstract
In this paper, we propose a continuous time equilibrium model of the (sellside) limit order book (LOB) in which the liquidity dynamics follows a non-local, reflected mean-field stochastic differential equation (SDE) with state-dependent intensity. To motivate the model we first study an N-seller static mean-field type Bertrand game among the liquidity providers. We shall then formulate the continuous time model as the limiting mean-field dynamics of the representative seller, and argue that the frontier of the LOB (e.g., the best ask price) is the value function of a mean-field stochastic control problem by the representative seller. Using a dynamic programming approach, we show that the value function is a viscosity solution of the corresponding Hamilton-Jacobi-Bellman equation, which can be used to determine the equilibrium density function of the LOB, in the spirit of [32].
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21 June 2022
The original version of the book was inadvertently published with incorrect abstracts in the chapters. This has now been amended.
In addition to this, the affiliation of author Dr. Bertram Tschiderer has been changed to Faculty of Mathematics, University of Vienna in the online version of Chapter 10.
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Ma, J., Noh, E. (2022). Equilibrium Model of Limit Order Books: A Mean-Field Game View. In: Yin, G., Zariphopoulou, T. (eds) Stochastic Analysis, Filtering, and Stochastic Optimization. Springer, Cham. https://doi.org/10.1007/978-3-030-98519-6_16
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DOI: https://doi.org/10.1007/978-3-030-98519-6_16
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Publisher Name: Springer, Cham
Print ISBN: 978-3-030-98518-9
Online ISBN: 978-3-030-98519-6
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