On an integral equation for the free-boundary of stochastic, irreversible investment problems
Ferrari, Giorgio
and El Karoui's representation theorem
one-dimensional diffusion
Bank
optimal stopping
stochastic control
singular
irreversible investment
free-boundary
Integral equation
base capacity
In this paper, we derive a new handy integral equation for the freeboundary of infinite time horizon, continuous time, stochastic, irreversible investment problems with uncertainty modeled as a one-dimensional, regular diffusion X. The new integral equation allows to explicitly find the freeboundary 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 [Ann. Probab. 32 (2004) 1030-1067]; then, thanks to such an identification and the fact that l* uniquely solves a backward stochastic equation, we find the integral problem for the free-boundary.
Institute Of Mathematical Statistics
2015
info:eu-repo/semantics/article
doc-type:article
text
https://pub.uni-bielefeld.de/record/2718995
Ferrari G. On an integral equation for the free-boundary of stochastic, irreversible investment problems. <em>The Annals of Applied Probability</em>. 2015;25(1):150-176.
eng
info:eu-repo/semantics/altIdentifier/doi/10.1214/13-AAP991
info:eu-repo/semantics/altIdentifier/issn/1050-5164
info:eu-repo/semantics/altIdentifier/wos/000347267400006
info:eu-repo/semantics/closedAccess