ON AN OPTIMAL EXTRACTION PROBLEM WITH REGIME SWITCHING

Ferrari G, Yang S (2018)
ADVANCES IN APPLIED PROBABILITY 50(3): 671-705.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
Download
Es wurde kein Volltext hochgeladen. Nur Publikationsnachweis!
Autor/in
;
Abstract / Bemerkung
In this paper we study a finite-fuel two-dimensional degenerate singular stochastic control problem under regime switching motivated by the optimal irreversible extraction problem of an exhaustible commodity. 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 cash flow, net of the costs of extraction and maintenance of the reserve. We provide expressions for both the value function and the optimal control. On the one hand, if the running cost for the maintenance of the reserve is a convex function of the reserve level, the optimal extraction rule prescribes a Skorokhod reflection of the (optimally) controlled state process at a certain state and price-dependent threshold. On the other hand, in the presence of a concave running cost function, it is optimal to instantaneously deplete the reserve at the time at which the commodity's price exceeds an endogenously determined critical level. In both cases, the threshold triggering the optimal control is given in terms of the optimal stopping boundary of an auxiliary family of perpetual optimal selling problems with regime switching.
Stichworte
Singular stochastic control; optimal stopping; regime switching; Hamilton-Jacobi-Bellman equation; free boundary; commodity extraction; optimal selling
Erscheinungsjahr
2018
Zeitschriftentitel
ADVANCES IN APPLIED PROBABILITY
Band
50
Ausgabe
3
Seite(n)
671-705
ISSN
0001-8678
eISSN
1475-6064
Page URI
https://pub.uni-bielefeld.de/record/2932800

Zitieren

Ferrari G, Yang S. ON AN OPTIMAL EXTRACTION PROBLEM WITH REGIME SWITCHING. ADVANCES IN APPLIED PROBABILITY. 2018;50(3):671-705.
Ferrari, G., & Yang, S. (2018). ON AN OPTIMAL EXTRACTION PROBLEM WITH REGIME SWITCHING. ADVANCES IN APPLIED PROBABILITY, 50(3), 671-705. doi:10.1017/apr.2018.31
Ferrari, G., and Yang, S. (2018). ON AN OPTIMAL EXTRACTION PROBLEM WITH REGIME SWITCHING. ADVANCES IN APPLIED PROBABILITY 50, 671-705.
Ferrari, G., & Yang, S., 2018. ON AN OPTIMAL EXTRACTION PROBLEM WITH REGIME SWITCHING. ADVANCES IN APPLIED PROBABILITY, 50(3), p 671-705.
G. Ferrari and S. Yang, “ON AN OPTIMAL EXTRACTION PROBLEM WITH REGIME SWITCHING”, ADVANCES IN APPLIED PROBABILITY, vol. 50, 2018, pp. 671-705.
Ferrari, G., Yang, S.: ON AN OPTIMAL EXTRACTION PROBLEM WITH REGIME SWITCHING. ADVANCES IN APPLIED PROBABILITY. 50, 671-705 (2018).
Ferrari, Giorgio, and Yang, Shuzhen. “ON AN OPTIMAL EXTRACTION PROBLEM WITH REGIME SWITCHING”. ADVANCES IN APPLIED PROBABILITY 50.3 (2018): 671-705.

Export

Markieren/ Markierung löschen
Markierte Publikationen

Open Data PUB

Web of Science

Dieser Datensatz im Web of Science®

Quellen

arXiv: 1602.06765

Suchen in

Google Scholar