Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/201639 
Year of Publication: 
2019
Series/Report no.: 
Center for Mathematical Economics Working Papers No. 614
Publisher: 
Bielefeld University, Center for Mathematical Economics (IMW), Bielefeld
Abstract: 
We study a class of infinite-dimensional singular stochastic control problems with applications in economic theory and finance. The control process linearly affects an abstract evolution equation on a suitable partially-ordered infinite-dimensional space X, it takes values in the positive cone of X, and it has right-continuous and nondecreasing paths. We first provide a rigorous formulation of the problem by properly defining the controlled dynamics and integrals with respect to the control process. We then exploit the concave structure of our problem and derive necessary and sufficient first-order conditions for optimality. The latter are finally exploited in a specification of the model where we find an explicit expression of the optimal control. The techniques used are those of semigroup theory, vector-valued integration, convex analysis, and general theory of stochastic processes.
Subjects: 
infinite-dimensional singular stochastic control
semigroup theory
vector-valued integration
first-order conditions
Bank-El Karoui's representation theorem
irreversible investment
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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