On an Integral Equation for the Free-Boundary of Stochastic, Irreversible Investment Problems
AbstractIn 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 mo-deled as a one-dimensional, regular diffusion X. The new integral equation allows to explicitly find the free-boundary b in some so far unsolved cases, as when the operating profit function is not multiplicatively separable and X is a three- dimensional Bessel process or a CEV process. Our result follows from purely probabilistic arguments. Indeed, we first show that b(X(t))=l(t), with l the unique optional solution of a representation problem in the spirit of Bank-El Karoui (2004); 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.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1211.0412.
Date of creation: Nov 2012
Date of revision: Jul 2013
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-11-11 (All new papers)
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