TY  - GEN
AB  - 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.
DA  - 2012
KW  - free boundary
KW  - irreversible investment
KW  - integral equation
KW  - singular stochastic control
KW  - Bank and El Karoui's Representation Theorem
KW  - one-dimensional diusion
KW  - optimal stopping
KW  - base capacity.
LA  - eng
PY  - 2012
SN  - 0931-6558
SP  - 20-
TI  - On an integral equation for the free boundary of stochastic, irreversible investment problems
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-26740341
Y2  - 2024-11-22T03:10:23
ER  -