A solvable two-dimensional degenerate singular stochastic control problem with non convex costs

Tiziano de Angelis, Giorgio Ferrari and John Moriarty
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Tiziano de Angelis: Center for Mathematical Economics, Bielefeld University
Giorgio Ferrari: Center for Mathematical Economics, Bielefeld University
John Moriarty: Center for Mathematical Economics, Bielefeld University

No 531, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

Abstract: In this paper we provide a complete theoretical analysis of a two-dimensional degenerate non convex 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 and the smooth fit condition holds there.

Keywords: finite-fuel singular stochastic control; optimal stopping; free boundary; Hamilton- Jacobi-Bellmann equation; irreversible investment; electricity market. (search for similar items in EconPapers)
Pages: 28
Date: 2016-03-16
New Economics Papers: this item is included in nep-ene
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https://pub.uni-bielefeld.de/download/2901687/2902044 First Version, 2014 (application/x-download)

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Persistent link: https://EconPapers.repec.org/RePEc:bie:wpaper:531

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