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

Giorgio Ferrari ()

No 471, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

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*(t), with 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* uniquely solves a backward stochastic equation, we find the integral problem for the free boundary.

Keywords: free boundary; irreversible investment; integral equation; singular stochastic control; Bank and El Karoui's Representation Theorem; one-dimensional di usion; optimal stopping; base capacity. (search for similar items in EconPapers)
Pages: 20
Date: 2014-04-29
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Citations: View citations in EconPapers (11)

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https://pub.uni-bielefeld.de/download/2674034/2674035 First Version, 2012 (application/pdf)

Related works:
Working Paper: On an integral equation for the free-boundary of stochastic, irreversible investment problems (2015)
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