Journal
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
Volume 52, Issue 4, Pages 2180-2223Publisher
SIAM PUBLICATIONS
DOI: 10.1137/130927814
Keywords
singular stochastic control; optimal capacity; reversible investment; viscosity solution; smooth fit
Categories
Funding
- Alma Research
- Chaire EDF-Calyon
- Finance and Developpement Durable
- FiME, Laboratoire de Finance des Marches de l'Energie
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This paper studies a reversible investment problem where a social planner aims to control its capacity production in order to fit optimally the random demand of a good. Our model allows for general diffusion dynamics on the demand as well as general cost functional. The resulting optimization problem leads to a degenerate two-dimensional bounded variation singular stochastic control problem, for which explicit solution is not available in general and the standard verification approach cannot be applied a priori. We use a direct viscosity solutions approach for deriving some features of the optimal free boundary function and for displaying the structure of the solution. In the quadratic cost case, we are able to prove a smooth fit C-2 property, which gives rise to a full characterization of the optimal boundaries and value function.
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