Convex duality for stochastic singular control problems

Citation
Bank, Peter et Kauppila, Helena, Convex duality for stochastic singular control problems, Annals of applied probability , 27(1), 2017, pp. 485-516
ISSN journal
10505164
Volume
27
Issue
1
Year of publication
2017
Pages
485 - 516
Database
ACNP
SICI code
Abstract
We develop a general theory of convex duality for certain singular control problems, taking the abstract results by Kramkov and Schachermayer [Ann. Appl. Probab. 9 (1999) 904-950] for optimal expected utility from nonnegative random variables to the level of optimal expected utility from increasing, adapted controls. The main contributions are the formulation of a suitable duality framework, the identification of the problem's dual functional as well as the full duality for the primal and dual value functions and their optimizers. The scope of our results is illustrated by an irreversible investment problem and the Hindy.Huang.Kreps utility maximization problem for incomplete financial markets.