---
_id: '2718995'
abstract:
- lang: eng
text: 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.
accept: '1'
additionalInformation: ISI import, vp
article_type: original
author:
- autoren_ansetzung:
- Ferrari, Giorgio
- Ferrari
- Giorgio Ferrari
- Ferrari, G
- Ferrari, G.
- G Ferrari
- G. Ferrari
first_name: Giorgio
full_name: Ferrari, Giorgio
id: '32701753'
last_name: Ferrari
citation:
ama: Ferrari G. On an integral equation for the free-boundary of stochastic, irreversible
investment problems. *The Annals of Applied Probability*. 2015;25(1):150-176.
angewandte-chemie: G. Ferrari, “On an integral equation for the free-boundary of
stochastic, irreversible investment problems”, *The Annals of Applied Probability*,
**2015**, *25*, 150-176.
apa: Ferrari, G. (2015). On an integral equation for the free-boundary of stochastic,
irreversible investment problems. *The Annals of Applied Probability*,
*25*(1), 150-176. doi:10.1214/13-AAP991
apa_indent: Ferrari,
G. (2015). On an integral equation for the free-boundary of stochastic, irreversible
investment problems. *The Annals of Applied Probability*, *25*(1),
150-176. doi:10.1214/13-AAP991

aps: ' G. Ferrari, On an integral equation for the free-boundary of stochastic,
irreversible investment problems, The Annals of Applied Probability **25**,
150 (2015).'
bio1: 'Ferrari G (2015)

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

The Annals of Applied Probability 25(1):
150-176.'
chicago: 'Ferrari,
Giorgio. 2015. “On an integral equation for the free-boundary of stochastic, irreversible
investment problems”. *The Annals of Applied Probability* 25 (1): 150-176.

'
default: 'Ferrari G (2015)

*The Annals of Applied Probability* 25(1):
150-176.'
dgps: Ferrari,
G. (2015). On an integral equation for the free-boundary of stochastic, irreversible
investment problems. *The Annals of Applied Probability*, *25*(1),
150-176. Institute Of Mathematical Statistics. doi:10.1214/13-AAP991.

frontiers: Ferrari, G. (2015). On an integral equation for the free-boundary of
stochastic, irreversible investment problems. *The Annals of Applied Probability*
25, 150-176.
harvard1: Ferrari, G., 2015. On an integral equation for the free-boundary of stochastic,
irreversible investment problems. *The Annals of Applied Probability*,
25(1), p 150-176.
ieee: ' G. Ferrari, “On an integral equation for the free-boundary of stochastic,
irreversible investment problems”, *The Annals of Applied Probability*, vol.
25, 2015, pp. 150-176.'
lncs: ' Ferrari, G.: On an integral equation for the free-boundary of stochastic,
irreversible investment problems. The Annals of Applied Probability. 25, 150-176
(2015).'
mla: 'Ferrari, Giorgio. “On an integral equation for the free-boundary of stochastic,
irreversible investment problems”. *The Annals of Applied Probability*
25.1 (2015): 150-176.'
wels: 'Ferrari, G. (2015): On an integral equation for the free-boundary of stochastic,
irreversible investment problems *The Annals of Applied Probability*,25:(1):
150-176.'
date_created: 2015-02-16T10:39:54Z
date_submitted: 2015-02-16T12:25:11Z
date_updated: 2018-07-24T13:01:24Z
department:
- _id: '10053'
doi: 10.1214/13-AAP991
external_id:
isi:
- '000347267400006'
first_author: Ferrari, Giorgio
id: '2718995'
intvolume: ' 25'
isi: 1
issue: '1'
keyword:
- and El Karoui's representation theorem
- one-dimensional diffusion
- Bank
- optimal stopping
- stochastic control
- singular
- irreversible investment
- free-boundary
- Integral equation
- base capacity
language:
- iso: eng
page: 150-176
publication: The Annals of Applied Probability
publication_identifier:
issn:
- 1050-5164
publication_status: published
publisher: Institute Of Mathematical Statistics
quality_controlled: '1'
status: public
title: On an integral equation for the free-boundary of stochastic, irreversible investment
problems
type: journal_article
volume: '25'
year: '2015'
...