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TITLE: [GS_M_APP] Stochastic Control and Free Boundary Problems Arising in Financial Mathematics

ABSTRACT: In this presentation, I discuss stochastic control problems arising from financial mathematics. Specifically, I address problems that combine stochastic control with optimal stopping, as well as those involving singular control and switching control. Furthermore, I investigate a two-person zero-sum game played between a singular controller and an optimal stopper. A key focus of this talk is deriving the associated parabolic variational inequalities and analyzing the analytic properties of the free boundaries they induce. I will also explain how these boundaries characterize the optimal strategies. Finally, I illustrate the application of these models in finance with numerical examples.