On an integral equation for the free boundary of stochastic, irreversible investment problems
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 ; 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.
|Date of creation:||29 Apr 2014|
|Date of revision:|
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- Maria B. Chiarolla & Giorgio Ferrari, 2011. "Identifying the Free Boundary of a Stochastic, Irreversible Investment Problem via the Bank-El Karoui Representation Theorem," Papers 1108.4886, arXiv.org, revised Dec 2013.
- Xia Su & Frank Riedel, 2006.
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- Steg, Jan-Henrik, 2011.
"Irreversible investment in oligopoly,"
Center for Mathematical Economics Working Papers
415, Center for Mathematical Economics, Bielefeld University.
- Ioannis Karatzas & Fridrik M. Baldursson, 1996. "Irreversible investment and industry equilibrium (*)," Finance and Stochastics, Springer, vol. 1(1), pages 69-89.
- Chiarolla, Maria B. & Ferrari, Giorgio & Riedel, Frank, 2014. "Generalized Kuhnâ€“Tucker conditions for N-Firm stochastic irreversible investment under limited resources," Center for Mathematical Economics Working Papers 463, Center for Mathematical Economics, Bielefeld University.
- Anders ûksendal, 2000. "Irreversible investment problems," Finance and Stochastics, Springer, vol. 4(2), pages 223-250.
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