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SUMMARY:Mean Field Game of Mutual Holding and systemic risk - Nizar Touzi 
 (Ecole Polytechnique Paris)
DTSTART:20220419T090000Z
DTEND:20220419T100000Z
UID:TALK171416@talks.cam.ac.uk
DESCRIPTION:We introduce a mean field model for optimal holding of a repre
 sentative agent of her peers as a natural expected scaling limit from the 
 corresponding N-agent model. The induced mean field dynamics appear natura
 lly in a form which is not covered by standard McKean-Vlasov stochastic di
 fferential equations. We study the corresponding mean field game of mutual
  holding in the absence of common noise. Our first main result provides an
  explicit equilibrium of this mean field game\, defined by a bang&ndash\;b
 ang control consisting in holding those competitors with positive drift co
 efficient of their dynamic value. We next use this mean field game equilib
 rium to construct (approximate) Nash equilibria for the corresponding&nbsp
 \;N&ndash\;player game. Finally\, we extend the model to allow for default
  upon hitting the origin. Then\, the equilibrium distribution exhibits an 
 atom at the origin whose mass evolution is characterized by a ordinary dif
 ferential equation.
LOCATION:Seminar Room 1\, Newton Institute
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