A non convex singular stochastic control problem and its related optimal stopping boundaries

Tiziano de Angelis, Giorgio Ferrari (giorgio.ferrari@uni-bielefeld.de) and John Moriarty
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Tiziano de Angelis: Center for Mathematical Economics, Bielefeld University
John Moriarty: Center for Mathematical Economics, Bielefeld University

No 508, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

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: finite-fuel singular stochastic control; optimal stopping; free-boundary; smooth- fit; Hamilton-Jacobi-Bellman equation; irreversible investment (search for similar items in EconPapers)
Pages: 25
Date: 2016-03-14
New Economics Papers: this item is included in nep-ore
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Citations: View citations in EconPapers (1)

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https://pub.uni-bielefeld.de/download/2901528/2902029 First Version, 2014 (application/x-download)

Related works:
Working Paper: A Non Convex Singular Stochastic Control Problem and its Related Optimal Stopping Boundaries (2014)
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Persistent link: https://EconPapers.repec.org/RePEc:bie:wpaper:508

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