Multidimensional singular control and related Skorokhod problem: Sufficient conditions for the characterization of optimal controls

Jodi Dianetti and Giorgio Ferrari

Stochastic Processes and their Applications, 2023, vol. 162, issue C, 547-592

Abstract: We characterize the optimal control for a class of singular stochastic control problems as the unique solution to a related Skorokhod reflection problem. The optimization problems concern the minimization of a discounted cost over an infinite time-horizon through a process of bounded variation affecting an Itô-diffusion. The setting is multidimensional, the drift of the state equation and the costs are convex, the volatility matrix can be constant or linear in the state. Our result applies to a relevant class of linear-quadratic models and it allows to construct the optimal control in degenerate and non degenerate settings considered in the literature.

Keywords: Dynkin games; Reflected diffusion; Singular stochastic control; Skorokhod problem; Variational inequalities (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2023.05.006

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