The Annals of Applied Probability

Convex duality for stochastic singular control problems

Peter Bank and Helena Kauppila

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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.

Article information

Source
Ann. Appl. Probab., Volume 27, Number 1 (2017), 485-516.

Dates
Received: October 2014
Revised: March 2016
First available in Project Euclid: 6 March 2017

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1488790833

Digital Object Identifier
doi:10.1214/16-AAP1209

Mathematical Reviews number (MathSciNet)
MR3619793

Zentralblatt MATH identifier
1360.93765

Subjects
Primary: 93E20: Optimal stochastic control 91G80: Financial applications of other theories (stochastic control, calculus of variations, PDE, SPDE, dynamical systems) 46N10: Applications in optimization, convex analysis, mathematical programming, economics 91B08: Individual preferences

Keywords
Convex duality singular control utility maximization irreversible investment incomplete markets

Citation

Bank, Peter; Kauppila, Helena. Convex duality for stochastic singular control problems. Ann. Appl. Probab. 27 (2017), no. 1, 485--516. doi:10.1214/16-AAP1209. https://projecteuclid.org/euclid.aoap/1488790833


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