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

25 Pages Posted: 11 May 2014 Last revised: 5 Dec 2014

See all articles by Tiziano De Angelis

Tiziano De Angelis

University of Manchester

Giorgio Ferrari

Bielefeld University - Center for Mathematical Economics

John Moriarty

Queen Mary University of London

Date Written: May 5, 2014

Abstract

We show that the equivalence between certain problems of singular stochastic control (SSC) and related questions of optimal stopping known for convex performance criteria (see, for example, Karatzas and Shreve (1984)) continues to hold in a non convex problem provided a related discretionary stopping time is introduced. Our problem is one of storage and consumption for electricity, a partially storable commodity with both positive and negative prices in some markets, and has similarities to the finite fuel monotone follower problem. In particular 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 the related optimal stopping boundaries.

Keywords: fi nite-fuel singular stochastic control, optimal stopping, free-boundary, smooth-fit, Hamilton-Jacobi-Bellman equation, irreversible investment

JEL Classification: C02, C61, E22, D92

Suggested Citation

De Angelis, Tiziano and Ferrari, Giorgio and Moriarty, John, A Non Convex Singular Stochastic Control Problem and Its Related Optimal Stopping Boundaries (May 5, 2014). Institute of Mathematical Economics Working Paper No. 508, Available at SSRN: https://ssrn.com/abstract=2435375 or http://dx.doi.org/10.2139/ssrn.2435375

Tiziano De Angelis

University of Manchester ( email )

Oxford Rd. M13 9PL
Manchester
United Kingdom

Giorgio Ferrari (Contact Author)

Bielefeld University - Center for Mathematical Economics ( email )

Postfach 10 01 31
Bielefeld, D-33501
Germany

John Moriarty

Queen Mary University of London ( email )

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