Abstract
Mean Field Games (MFG) theory is a recent branch of Dynamic Games aiming at modelling and solving complex decision processes involving a large number of agents which are each other influencing. The MFG framework has been recently applied to the known optimal trading problem. In the original model (see Cardaliaguet and Lehalle [1]), the Authors consider an optimal trading model where a continuum of homogeneous investors make trades on one single financial instrument. Each participant acts strategically controlling her trading speed given the information she has concerning the behaviour of the others in order to fulfil her goal. This leads to a MFG equilibrium in which the mean field depends on the agents’ actions. In this paper, we present an MFG-based model in which the maximum intensity of the trading speed depends on the available information flow and is modelled as a piecewise linear properly saturated function.
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Notes
- 1.
The constant part of the cost is firstly introduced in this paper.
- 2.
Similar arguments hold for the representation of v in the last branch of (7), hence when \(u^*=u_m(\xi )\).
References
Cardaliaguet, P., Lehalle, C.A.: Mean field game of controls and an application to trade crowding. Math. Finan. Econ. 12, 335–363 (2018)
Cartea, Á., Jaimungal, S.: Incorporating order-flow into optimal execution. Math. Finan. Econ. 10, 339–364 (2016)
Gomes, D.A., Patrizi, S., Voskanyan, V.: On the existence of classical solutions for stationary extended mean field games. Nonlinear Anal. Theory Methods Appl. 99, 49–79 (2014)
Lasry, J.-M., Lions, P.-L.: Mean field games. Jpn. J. Math. 2(1), 229–260 (2007)
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Corazza, M., Maggistro, R., Pesenti, R. (2021). MFG-Based Trading Model with Information Costs. In: Corazza, M., Gilli, M., Perna, C., Pizzi, C., Sibillo, M. (eds) Mathematical and Statistical Methods for Actuarial Sciences and Finance. Springer, Cham. https://doi.org/10.1007/978-3-030-78965-7_23
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DOI: https://doi.org/10.1007/978-3-030-78965-7_23
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