Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/81090
Authors: 
Ferrari, Giorgio
Year of Publication: 
2012
Series/Report no.: 
Working Papers, Institute of Mathematical Economics 471
Abstract: 
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.
Subjects: 
integral equation
free boundary
irreversible investment
singular stochastic control
optimal stopping
one-dimensional diffusion
Bank and El Karoui's Representation Theorem
base capacity
JEL: 
C02
E22
D92
G31
Document Type: 
Working Paper

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