On an integral equation for the free boundary of stochastic, irreversible investment problems

Arbeitspapier

In this paper we derive a new handy integral equation for the free boundary of infinite time horizon, continuous time, stochastic, irreversible investment problems with uncertainty modeled as a one-dimensional, regular diffusion X0;x. The new integral equation allows to explicitly find the free boundary b(.) in some so far unsolved cases, as when X0;x is a three-dimensional Bessel process or a CEV process. Our result follows from purely probabilistic arguments. Indeed, we first show that b(X0;x(t)) = l L(t), with l L(t) unique optional solution of a representation problem in the spirit of Bank-El Karoui [4]; then, thanks to such identification and the fact that l L uniquely solves a backward stochastic equation, we find the integral problem for the free boundary.

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• Sprache: Englisch

Verweise und Beziehungen

• Erschienen in: Series: Working Papers ; No. 471

Klassifikation und Themen

• Klassifikation: Wirtschaft ; Mathematical Methods ; Investment; Capital; Intangible Capital; Capacity ; Capital Budgeting; Fixed Investment and Inventory Studies; Capacity
• Thema: integral equation ; free boundary ; irreversible investment ; singular stochastic control ; optimal stopping ; one-dimensional diffusion ; Bank and El Karoui's Representation Theorem ; base capacity

Beteiligte, Orts- und Zeitangaben

• Ereignis: Geistige Schöpfung
• (wer): Ferrari, Giorgio
• Ereignis: Veröffentlichung
• (wer): Bielefeld University, Institute of Mathematical Economics (IMW)
• (wo): Bielefeld
• (wann): 2012

Weitere Informationen

• Handle: http://hdl.handle.net/10419/81090
• URN: urn:nbn:de:0070-pub-26740341