• Corpus ID: 159168976

# A Mean Field Game Of Portfolio Trading And Its Consequences On Perceived Correlations

@article{Lehalle2019AMF,
title={A Mean Field Game Of Portfolio Trading And Its Consequences On Perceived Correlations},
author={Charles-Albert Lehalle and Charafeddine Mouzouni},
year={2019}
}
• Published 31 January 2019
• Economics
• arXiv: Trading and Market Microstructure
This paper goes beyond the optimal trading Mean Field Game model introduced by Pierre Cardaliaguet and Charles-Albert Lehalle in [Cardaliaguet, P. and Lehalle, C.-A., Mean field game of controls and an application to trade crowding, Mathematics and Financial Economics (2018)]. It starts by extending it to portfolios of correlated instruments. This leads to several original contributions: first that hedging strategies naturally stem from optimal liquidation schemes on portfolios. Second we show…
22 Citations

## Figures and Tables from this paper

• Mathematics
Math. Oper. Res.
• 2021
This work proves that the solution to the mean field game (MFG) can be characterized in terms of a forward-backward stochastic differential equation (FBSDE) with a possibly singular terminal condition on the backward component or, equivalently, on an FBSDE with a finite terminal value yet a singular driver.
• Economics, Mathematics
SIAM J. Control. Optim.
• 2022
In this work, we study an equilibrium-based continuous asset pricing problem which seeks to form a price process endogenously by requiring it to balance the flow of sales-and-purchase orders in the
• Mathematics, Economics
• 2020
We investigate the problem of equilibrium price formation in an incomplete securities market. Each financial firm (agent) tries to minimize its cost via continuous-time trading with a securities
• Economics
SSRN Electronic Journal
• 2021
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
• Economics
ArXiv
• 2018
This work uses filtering techniques coupled with a convex analysis approach to solve the mean field game limit of the problem, and demonstrates that the best response strategies generate an $\epsilon$-Nash equilibrium for finite populations.
• Economics
Mathematical Finance
• 2022
This work characterize firms’ optimal controls as the solution of McKean-Vlasov (MV) FBSDEs and determine the equilibrium SREC price, and establishes the existence and uniqueness of a solution to this MV-FBSDE, and proves that the MFG strategies form an -Nash equilibrium for the finite player game.
• Economics
ArXiv
• 2020
This work forms a stochastic control problem for generating and trading in SREC markets from a regulated firm’s perspective, provides a characterization of the optimal strategy and develops a numerical algorithm to solve this control problem.
• Mathematics, Economics
SIAM J. Financial Math.
• 2022
We study an equilibrium-based continuous asset pricing problem for the securities market. In the previous work [16], we have shown that a certain price process, which is given by the solution to a
• Economics, Computer Science
2022 American Control Conference (ACC)
• 2022
This work considers entropy-regularized mean-field games with a finite state-action space in a discrete time setting and shows that entropy regularization provides the necessary regularity conditions, that are lacking in the standard finite mean field games.
• Economics
• 2021
. Principal agent games are a growing area of research which focuses on the optimal behaviour of a principal and an agent, with the former contracting work from the latter, in return for providing a

## References

SHOWING 1-10 OF 36 REFERENCES

• Economics
• 2016
In this paper we formulate the now classical problem of optimal liquidation (or optimal trading) inside a mean field game (MFG). This is a noticeable change since usually mathematical frameworks
• Economics
• 2011
We propose a simple multiperiod model of price impact from trading in a market with multiple assets, which illustrates how feedback effects due to distressed selling and short selling lead to
• Economics
• 2010
We solve a multi-period model of strategic trading with long-lived information in multiple assets with correlated innovations in fundamental values. Market makers in each asset can only condition
• Economics
Applied Mathematical Finance
• 2019
ABSTRACT Algorithmic trading strategies for execution often focus on the individual agent who is liquidating/acquiring shares. When generalized to multiple agents, the resulting stochastic game is
• Economics
• 2016
The vast majority of market impact studies assess each product individually, and the interactions between the different order flows are disregarded. This strong approximation may lead to an
• Economics
SIAM J. Financial Math.
• 2012
The interactions of limit orders with the market are modeled via a Poisson process pegged to a diffusive "fair price" and a Hamilton-Jacobi-Bellman equation is used to solve the problem involving both non-execution risk and price risk.
• Economics
• 2000
This paper explicitly constructs the efficient frontier in the space of time-dependent liquidation strategies, which have minimum expected cost for a given level of uncertainty, and leads to the concept of Liquidity-adjusted VAR, or L-VaR, that explicitly considers the best tradeoff between volatility risk and liquidation costs.
• Economics
• 2017
We model the impact costs of a strategy that trades a basket of correlated instruments, by extending to the multivariate case the linear propagator model previously used for single instruments. Our
• Economics
• 2005
The impact of large trades on market prices is a widely discussed but rarely measured phenomenon, of essential importance to selland buy-side participants. We analyse a large data set from the
• Economics
SIAM J. Financial Math.
• 2010
The main results show that, under general conditions on the shape function of the limit order book, placing deterministic trade sizes at trading dates that are homogeneously spaced is optimal within a large class of adaptive strategies with arbitrary trading dates.