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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Center for Mathematical Economics Working Papers ; No. 509

Classification and Topics

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

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): De Angelis, Tiziano ; Federico, Salvatore ; Ferrari, Giorgio
• Event: Veröffentlichung
• (who): Bielefeld University, Center for Mathematical Economics (IMW)
• (where): Bielefeld
• (when): 2014

Further information

• DOI: doi:10.2139/ssrn.2458910
• Handle: http://hdl.handle.net/10419/103927
• Last update: 10.03.2025, 11:42 AM CET