| Issue |
ESAIM: COCV
Volume 28, 2022
|
|
|---|---|---|
| Article Number | 21 | |
| Number of page(s) | 36 | |
| DOI | https://doi.org/10.1051/cocv/2022015 | |
| Published online | 08 March 2022 | |
Equilibrium price formation with a major player and its mean field limit*
Quantitative Finance Course, Graduate School of Economics, The University of Tokyo,
Tokyo, Japan.
** Corresponding author: mfujii@e.u-tokyo.ac.jp
Received:
7
April
2021
Accepted:
12
February
2022
In this article, we consider the problem of equilibrium price formation in an incomplete securities market consisting of one major financial firm and a large number of minor firms. They carry out continuous trading via the securities exchange to minimize their cost while facing idiosyncratic and common noises as well as stochastic order flows from their individual clients. The equilibrium price process that balances demand and supply of the securities, including the functional form of the price impact for the major firm, is derived endogenously both in the market of finite population size and in the corresponding mean field limit.
Mathematics Subject Classification: 49N80 / 91A16 / 91B50 / 91B70
Key words: Mean field game / major agent / mean-field type control / controlled-FBSDEs / equilibrium price formation / market clearing
© The authors. Published by EDP Sciences, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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