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Séminaire informel de théorie des systèmes (ISS)

A mean field game - Hybrid systems approach to optimal execution problems in finance with stopping times

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19 jan. 2018   11h00 — 12h00

Dena Firoozi Université McGill, Canada

This work is about combining two major contemporary systems and control methodologies to obtain a unique E-Nash equilibrium for optimal execution problems within the stock market, namely Mean Field Game (MFG) theory and Hybrid Optimal Control (HOC) theory. Following standard financial models, the stock market is studied in this paper as a large population non-cooperative game where each trader has stochastic linear dynamics with quadratic costs. We consider the case where there exists one major trader with significant influence on market movements together with a large number of minor traders (within two subpopulations), each with individually asymptotically negligible effect on the market. The traders are coupled in their dynamics and cost functions by the market's average trading rate (a component of the system mean field) and the hybrid feature enters via the indexing of the cessation of trading by one or both subpopulations of minor traders by discrete states. Optimal stopping time strategies together with best response trading policies for all traders are established with respect to their individual cost criteria by an application of LQG HOC theory.


Entrée gratuite
Bienvenue à tous!

Peter E. Caines responsable
Aditya Mahajan responsable
Dena Firoozi responsable

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Salle MC 437
CIM
Pavillon McConnell
Université McGill
3480, rue University Montréal QC H3A 0E9 Canada

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