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Federico, Salavatore
Ferrari, Giorgio
Schuhmann, Patrick
Year of Publication: 
Series/Report no.: 
Center for Mathematical Economics Working Papers No. 637
We consider a standard Brownian motion whose drift can be increased or decreased in a possibly singular manner. The objective is to minimize an expected functional involving the time-integral of a running cost and the proportional costs of adjusting the drift. The resulting two-dimensional degenerate singular stochastic control problem is solved by combining techniques of viscosity theory and free boundary problems. We provide a detailed description of the problem's value function and of the geometry of the state space, which is split into three regions by two monotone curves. Our main result shows that those curves are continuously differentiable with locally Lipschitz derivative and solve a system of nonlinear ordinary differential equations.
singular stochastic control
Dynkin game
viscosity solution
free boundary
Brownian motion
ordinary differential equation
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Working Paper

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