On an optimal extraction problem with regime switching

Giorgio Ferrari and Shuzhen Yang
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Giorgio Ferrari: Center for Mathematical Economics, Bielefeld University
Shuzhen Yang: Center for Mathematical Economics, Bielefeld University

No 562, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

Abstract: This paper studies an optimal irreversible extraction problem of an exhaustible commodity in presence of regime shifts. A company extracts a natural resource from a reserve with finite capacity, and sells it in the market at a spot price that evolves according to a Brownian motion with volatility modulated by a two state Markov chain. In this setting, the company aims at finding the extraction rule that maximizes its expected, discounted net cash flow. The problem is set up as a finite-fuel two-dimensional degenerate singular stochastic control problem over an infinite time-horizon. We provide explicit expressions both for the value function and for the optimal control. We show that the latter prescribes a Skorokhod reflection of the optimally controlled state process at a certain state and price dependent threshold. This curve is given in terms of the optimal stopping boundary of an auxiliary family of perpetual optimal selling problems with regime switching. The techniques are those of stochastic calculus and stochastic optimal control theory.

Keywords: singular stochastic control; optimal stopping; regime switching; Hamilton-Jacobi-Bellman equation; free-boundary; commodity extraction; optimal selling (search for similar items in EconPapers)
Pages: 31
Date: 2016-07-20
New Economics Papers: this item is included in nep-ene
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