On the Optimal Boundary of a Three-Dimensional Singular Stochastic Control Problem Arising in Irreversible Investment

Arbeitspapier

This paper examines a Markovian model for the optimal irreversible investment problem of a firm aiming at minimizing total expected costs of production. We model market uncertainty and the cost of investment per unit of production capacity as two independent one-dimensional regular diffusions, and we consider a general convex running cost function. The optimization problem is set as a three-dimensional degenerate singular stochastic control problem. We provide the optimal control as the solution of a Skorohod reflection problem at a suitable free-boundary surface. Such boundary arises from the analysis of a family of two-dimensional parameter-dependent optimal stopping problems and it is characterized in terms of the family of unique continuous solutions to parameter-dependent nonlinear integral equations of Fredholm type.

Angaben zum Objekt

• Sprache: Englisch

Verweise und Beziehungen

• Erschienen in: Series: Center for Mathematical Economics Working Papers ; No. 509

Klassifikation und Themen

• Klassifikation: Wirtschaft ; Mathematical Methods ; Stochastic and Dynamic Games; Evolutionary Games; Repeated Games ; Investment; Capital; Intangible Capital; Capacity
• Thema: irreversible investment ; singular stochastic control ; optimal stopping ; free-boundary problems ; nonlinear integral equations

Beteiligte, Orts- und Zeitangaben

• Ereignis: Geistige Schöpfung
• (wer): De Angelis, Tiziano ; Federico, Salvatore ; Ferrari, Giorgio
• Ereignis: Veröffentlichung
• (wer): Bielefeld University, Center for Mathematical Economics (IMW)
• (wo): Bielefeld
• (wann): 2014

Weitere Informationen

• DOI: doi:10.2139/ssrn.2458910
• Handle: http://hdl.handle.net/10419/103927
• Letzte Aktualisierung: 10.03.2025, 11:42 MEZ