A Non Convex Singular Stochastic Control Problem and its Related Optimal Stopping Boundaries

Tiziano De Angelis, Giorgio Ferrari () and John Moriarty

Papers from arXiv.org

Abstract: Equivalences are known between problems of singular stochastic control (SSC) with convex performance criteria and related questions of optimal stopping, see for example Karatzas and Shreve [SIAM J. Control Optim. 22 (1984)]. The aim of this paper is to investigate how far connections of this type generalise to a non convex problem of purchasing electricity. Where the classical equivalence breaks down we provide alternative connections to optimal stopping problems. We consider a non convex infinite time horizon SSC problem whose state consists of an uncontrolled diffusion representing a real-valued commodity price, and a controlled increasing bounded process representing an inventory. We analyse the geometry of the action and inaction regions by characterising their (optimal) boundaries. Unlike the case of convex SSC problems we find that the optimal boundaries may be both reflecting and repelling and it is natural to interpret the problem as one of SSC with discretionary stopping.

Date: 2014-05, Revised 2014-11
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (10)

Downloads: (external link)
http://arxiv.org/pdf/1405.2442 Latest version (application/pdf)

Related works:
Working Paper: A non convex singular stochastic control problem and its related optimal stopping boundaries (2016)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1405.2442

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().