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}, journal={arXiv: Trading and Market Microstructure}, year={2019} }
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…
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References
SHOWING 1-10 OF 36 REFERENCES
Mean field game of controls and an application to trade crowding
- 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…
RUNNING FOR THE EXIT: DISTRESSED SELLING AND ENDOGENOUS CORRELATION IN FINANCIAL MARKETS
- 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…
Informed Trading and Portfolio Returns
- 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…
Mean-Field Game Strategies for Optimal Execution
- EconomicsApplied 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…
Dissecting cross-impact on stock markets: an empirical analysis
- 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…
Optimal Portfolio Liquidation with Limit Orders
- EconomicsSIAM 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.
Optimal execution of portfolio trans-actions
- 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.
Trading Lightly: Cross-Impact and Optimal Portfolio Execution
- 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…
Direct Estimation of Equity Market Impact
- 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…
Optimal Trade Execution and Absence of Price Manipulations in Limit Order Book Models
- EconomicsSIAM 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.