Abstract

We study an equilibrium-based continuous asset pricing problem for the securities market. In the previous work [M. Fujii and A. Takahashi (2022), SIAM J. Control Optim., 60, pp. 259--279], we have shown that a certain price process, which is given by the solution to a forward-backward stochastic differential equation of conditional McKean--Vlasov type, asymptotically clears the market in the large population limit. In the current work, under suitable conditions, we show the existence of a finite agent equilibrium and its strong convergence to the corresponding mean-field limit given in [M. Fujii and A. Takahashi (2022), SIAM J. Control Optim., 60, pp. 259--279]. As an important byproduct, we get the direct estimate on the difference of the equilibrium price between the two markets: the one consisting of heterogeneous agents of finite population size and the other of homogeneous agents of infinite population size.

Keywords

  1. mean field games
  2. equilibrium in incomplete markets
  3. common noise
  4. market clearing
  5. price formation

MSC codes

  1. 91A15
  2. 91A16

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Information

Published In

cover image SIAM Journal on Financial Mathematics
SIAM Journal on Financial Mathematics
Pages: 459 - 490
ISSN (online): 1945-497X

History

Submitted: 17 August 2021
Accepted: 9 December 2021
Published online: 28 April 2022

Keywords

  1. mean field games
  2. equilibrium in incomplete markets
  3. common noise
  4. market clearing
  5. price formation

MSC codes

  1. 91A15
  2. 91A16

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