Probability and Mathematical Physics Seminar

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Viscosity Solutions for HJB Equations on the Process Space: Application to Mean Field Control with Common Noise

Speaker: Nizar Touzi, NYU

Location: Columbia University, Mathematics Hall, 2990 Broadway 207

Date: Friday, February 9, 2024, 11 a.m.

Synopsis:

In this paper we investigate a path dependent optimal control problem on the process space with both drift and volatility controls, with possibly degenerate volatility. The dynamic value function is characterized by a fully nonlinear second order path dependent HJB equation on the process space, which is by nature infinite dimensional. In particular, our model covers mean field control problems with common noise as a special case. We introduce a new notion of viscosity solutions and establish both existence and comparison principle, under merely Lipschitz continuity assumptions.

Notes:

Probability and the City seminar