Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/238123
Year of Publication: 
2021
Series/Report no.: 
Center for Mathematical Economics Working Papers No. 645
Publisher: 
Bielefeld University, Center for Mathematical Economics (IMW), Bielefeld
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 considered optimization problems concern the minimization of a discounted cost functional over an infinite time-horizon through a process of bounded variation affecting an Itô-diffusion. The setting is multidimensional, the dynamics of the state and the costs are convex, the volatility matrix can be constant or linear in the state. We prove that the optimal control acts only when the underlying diffusion attempts to exit the so-called waiting region, and that the direction of this action is prescribed by the derivative of the value function. Our approach is based on the study of a suitable monotonicity property of the derivative of the value function through its interpretation as the value of an optimal stopping game. Such a monotonicity allows to construct nearly optimal policies which reflect the underlying diffusion at the boundary of approximating waiting regions. The limit of this approximation scheme then provides the desired characterization. Our result applies to a relevant class of linear-quadratic models, among others. Furthermore, it allows to construct the optimal control in degenerate and non degenerate settings considered in the literature, where this important aspect was only partially addressed.
Subjects: 
Dynkin games
reflected diffusion
singular stochastic control
Skorokhod problem
variational inequalities
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Working Paper

Files in This Item:
File
Size





Items in EconStor are protected by copyright, with all rights reserved, unless otherwise indicated.