TY  - GEN
AB  - 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.
DA  - 2016
KW  - singular stochastic control
KW  - optimal stopping
KW  - regime switching
KW  - Hamilton-Jacobi-Bellman equation
KW  - free-boundary
KW  - commodity extraction
KW  - optimal selling
LA  - eng
PY  - 2016
SN  - 0931-6558
SP  - 31-
TI  - On an optimal extraction problem with regime switching
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-29047319
Y2  - 2024-11-22T02:24:03
ER  -