A Mean Field Game of Optimal Portfolio Liquidation

Fu, Guanxing; Graewe, Paulwin; Horst, Ulrich; Popier, Alexandre

doi:10.1287/moor.2020.1094

Cited by 42 publications

(84 citation statements)

References 33 publications

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“…We here recall some basic facts concerning Hölder continuous functions and provide a proof of the explicit solution to the product log equation (33).…”

Section: Appendixmentioning

confidence: 99%

“…For such reason, a more general class of MFG systems were introduced in [34] under the terminology of extended MFG models or mean-field of control to allow for stochastic dynamics depending upon the joint distribution of the controlled state and the control process. The mean-field of control setting allowed the authors of [24] to analyze optimal liquidation strategies in a context where trader's choices affect the public price of a good, and has since been employed by several authors [1,9,33]. Existence and uniqueness results for mean-field of controls on T d were discussed in the recente work [40].…”

Section: Introductionmentioning

confidence: 99%

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Mean Field Games of Controls with Dirichlet boundary conditions

Bongini¹,

Salvarani²

2021

Preprint

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In this paper we study a mean-field games system with Dirichlet boundary conditions in a closed domain and in a mean-field of control setting, that is in which the dynamics of each agent is affected not only by the average position of the rest of the agents but also by their average optimal choice. This setting allows the modeling of more realistic real-life scenarios in which agents not only will leave the domain at a certain point in time (like during the evacuation of pedestrians or in debt refinancing dynamics) but also act competitively to anticipate the strategies of the other agents. We shall establish the existence of Nash Equilibria for such class of mean-field of controls systems under certain regularity assumptions on the dynamics and the Lagrangian cost. Much of the paper is devoted to establishing several a priori estimates which are needed to circumvent the fact that the mass is not conserved (as we are in a Dirichlet boundary condition setting). In the conclusive sections, we provide examples of systems falling into our framework as well as numerical implementations.

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“…We here recall some basic facts concerning Hölder continuous functions and provide a proof of the explicit solution to the product log equation (33).…”

Section: Appendixmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Mean Field Games of Controls with Dirichlet boundary conditions

Bongini¹,

Salvarani²

2021

Preprint

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“…When all agents deploy the policy π of the representative agent, a new mean field flow is induced and can be propagated via (11) starting from µ 0 . We use the operator B prop : Π → M to denote this propagation.…”

Section: A Representative Agentmentioning

confidence: 99%

Shaping Large Population Agent Behaviors Through Entropy-Regularized Mean-Field Games

Guan

Zhou

Pakniyat

et al. 2021

Preprint

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Mean-field games (MFG) were introduced to efficiently analyze approximate Nash equilibria in large population settings. In this work, we consider entropy-regularized meanfield games with a finite state-action space in a discrete time setting. We show that entropy regularization provides the necessary regularity conditions, that are lacking in the standard finite mean field games. Such regularity conditions enable us to design fixed-point iteration algorithms to find the unique meanfield equilibrium (MFE). Furthermore, the reference policy used in the regularization provides an extra means, through which one can control the behavior of the population. We first formulate the problem as a stochastic game with a large population of N homogeneous agents. We establish conditions for the existence of a Nash equilibrium in the limiting case as N tends to infinity, and we demonstrate that the Nash equilibrium for the infinite population case is also an -Nash equilibrium for the N -agent regularized game, where the sub-optimality is of order O 1/ √ N . Finally, we verify the theoretical guarantees through a resource allocation example and demonstrate the efficacy of using a reference policy to control the behavior of a large population of agents.

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“…Even more tractable results obtain in the mean-field limit of many small agents, which often reduces the analysis to single-agent stochastic control problems with the average of all agents actions acting as an additional exogenous input. In the present context, such models have been studied by Cardaliaguet and Lehalle (2018); Jaimungal (2019, 2020); Fu, Graewe, Horst, and Popier (2021); Neuman and Voß (2021), for example.…”

Section: Introductionmentioning

confidence: 98%

Closed-Loop Nash Competition for Liquidity

Micheli¹,

Muhle‐Karbe²,

Neuman³

2021

Preprint

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We study a multi-player stochastic differential game, where agents interact through their joint price impact on an asset that they trade to exploit a common trading signal. In this context, we prove that a closed-loop Nash equilibrium exists if the price impact parameter is small enough. Compared to the corresponding open-loop Nash equilibrium, both the agents' optimal trading rates and their performance move towards the central-planner solution, in that excessive trading due to lack of coordination is reduced. However, the size of this effect is modest for plausible parameter values.

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A Mean Field Game of Optimal Portfolio Liquidation

Cited by 42 publications

References 33 publications

Mean Field Games of Controls with Dirichlet boundary conditions

Mean Field Games of Controls with Dirichlet boundary conditions

Shaping Large Population Agent Behaviors Through Entropy-Regularized Mean-Field Games

Closed-Loop Nash Competition for Liquidity

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