Nonlinear partial differential equation and stochastic singular control

Ryan Hynd (November 6, 2010)

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Abstract

Nonlinear partial differential equations arise in stochastic optimal control via dynamic programming equations. In many cases, solutions of these equations aid in the design of optimal controls. We discuss a class of equations where the associated control processes are "singular" with respect to the time variable. These equations arise in models for spacecraft control, financial models that incorporate transaction costs, and in models of queueing systems.