A Solvable Two-Dimensional Degenerate Singular Stochastic Control Problem with Nonconvex Costs

Tiziano De Angelis (), Giorgio Ferrari () and John Moriarty ()
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Tiziano De Angelis: School of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom
Giorgio Ferrari: Center for Mathematical Economics, Bielefeld University, D-33615 Bielefeld, Germany
John Moriarty: School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom

Mathematics of Operations Research, 2019, vol. 44, issue 2, 512-531

Abstract: In this paper we provide a complete theoretical analysis of a two-dimensional degenerate nonconvex singular stochastic control problem. The optimisation is motivated by a storage-consumption model in an electricity market, and features a stochastic real-valued spot price modelled by Brownian motion. We find analytical expressions for the value function, the optimal control, and the boundaries of the action and inaction regions. The optimal policy is characterised in terms of two monotone and discontinuous repelling free boundaries, although part of one boundary is constant and the smooth fit condition holds there.

Keywords: finite-fuel singular stochastic control; optimal stopping; free boundary; Hamilton–Jacobi–Bellman equation; irreversible investment; electricity market (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (8)

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