A stochastic reversible investment problem on a finite-time horizon: Free boundary analysis

Arbeitspapier

We study a continuous-time, finite horizon optimal stochastic reversible investment problem for a firm producing a single good. The production capacity is modeled as a onedimensional,time-homogeneous, linear diffusion controlled by a bounded variation process which represents the cumulative investment-disinvestment strategy. We associate to the investmentdisinvestment problem a zero-sum optimal stopping game and characterize its value function through a free boundary problem with two moving boundaries. These are continuous, bounded and monotone curves that solve a system of non-linear integral equations of Volterra type. The optimal investment-disinvestment strategy is then shown to be a diff usion reflected at the two boundaries.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Working Papers ; No. 477

Classification and Topics

• Classification: Wirtschaft ; Mathematical Methods ; Stochastic and Dynamic Games; Evolutionary Games; Repeated Games ; Investment; Capital; Intangible Capital; Capacity
• Subject: reversible investment ; singular stochastic control ; zero-sum optimal stopping games ; free boundary problems ; Skorokhod reflection problem

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): De Angelis, Tiziano ; Ferrari, Giorgio
• Event: Veröffentlichung
• (who): Bielefeld University, Institute of Mathematical Economics (IMW)
• (where): Bielefeld
• (when): 2013

Further information

• Handle: http://hdl.handle.net/10419/81115
• URN: urn:nbn:de:0070-pub-26740839
• Last update: 10.03.2025, 11:44 AM CET