Set Valued Hamilton-Jacobi-Bellman Equations - Applications and Theory

Explore the concept of set-valued partial differential equations (PDEs) in this USC Probability and Statistics Seminar talk. Delve into the applications of set values in time-inconsistent stochastic optimization problems, multivariate dynamic risk measures, and nonzero sum games with multiple equilibria. Examine the crucial dynamic programming principle (DPP) and its relationship with the set-valued Itô formula in inducing PDEs. Investigate the introduction of set-valued Hamilton-Jacobi-Bellman (HJB) equations in the context of multivariate optimization problems and their wellposedness. Learn how these set-valued PDEs reduce to standard HJB equations in scalar cases. Discover the connections between this approach and the theory of surface evolution equations, such as mean curvature flows, and understand the distinctions in their applications and time orientations. Gain insights into the extension of first-order set-valued ODEs to second-order PDEs and the implications of backward equations with terminal conditions in this field.