Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/149019
Authors: 
Ferrari, Giorgio
Yang, Shuzhen
Year of Publication: 
2016
Series/Report no.: 
Working Papers, Center for Mathematical Economics 562
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.
Subjects: 
singular stochastic control
optimal stopping
regime switching
Hamilton-Jacobi-Bellman equation
free-boundary
commodity extraction
optimal selling
JEL: 
C61
Q32
G11
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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