article
On an integral equation for the free-boundary of stochastic, irreversible investment problems
published
yes
Giorgio
Ferrari
author 32701753
10053
department
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 Statistics2015
eng
and El Karoui's representation theoremone-dimensional diffusionBankoptimal stoppingstochastic controlsingularirreversible investmentfree-boundaryIntegral equationbase capacity
The Annals of Applied Probability
1050-5164
00034726740000610.1214/13-AAP991
251150-176
Ferrari G (2015) <br />On an integral equation for the free-boundary of stochastic, irreversible investment problems.<br />The Annals of Applied Probability 25(1): 150-176.
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.
<div style="text-indent:-25px; padding-left:25px;padding-bottom:0px;">Ferrari, G. (2015). On an integral equation for the free-boundary of stochastic, irreversible investment problems. <em>The Annals of Applied Probability</em>, <em>25</em>(1), 150-176. doi:10.1214/13-AAP991</div>
<div style="text-indent:-25px; padding-left:25px;padding-bottom:0px;">Ferrari, Giorgio. 2015. “On an integral equation for the free-boundary of stochastic, irreversible investment problems”. <em>The Annals of Applied Probability</em> 25 (1): 150-176.</div>
G. Ferrari, “On an integral equation for the free-boundary of stochastic, irreversible investment problems”, <em>The Annals of Applied Probability</em>, vol. 25, 2015, pp. 150-176.
Ferrari G (2015) <br /><em>The Annals of Applied Probability</em> 25(1): 150-176.
Ferrari, Giorgio. “On an integral equation for the free-boundary of stochastic, irreversible investment problems”. <em>The Annals of Applied Probability</em> 25.1 (2015): 150-176.
<div style="text-indent:-25px; padding-left:25px;padding-bottom:0px;">Ferrari, G. (2015). On an integral equation for the free-boundary of stochastic, irreversible investment problems. <em>The Annals of Applied Probability</em>, <em>25</em>(1), 150-176. Institute Of Mathematical Statistics. doi:10.1214/13-AAP991.</div>
G. Ferrari, “On an integral equation for the free-boundary of stochastic, irreversible investment problems”, <em>The Annals of Applied Probability</em>, <strong>2015</strong>, <em>25</em>, 150-176.
Ferrari, G. (2015). On an integral equation for the free-boundary of stochastic, irreversible investment problems. <em>The Annals of Applied Probability</em>, <em>25</em>(1), 150-176. doi:10.1214/13-AAP991
G. Ferrari, On an integral equation for the free-boundary of stochastic, irreversible investment problems, The Annals of Applied Probability <strong>25</strong>, 150 (2015).
Ferrari, G. (2015): On an integral equation for the free-boundary of stochastic, irreversible investment problems <em>The Annals of Applied Probability</em>,25:(1): 150-176.
Ferrari, G., 2015. On an integral equation for the free-boundary of stochastic, irreversible investment problems. <em>The Annals of Applied Probability</em>, 25(1), p 150-176.
Ferrari, G. (2015). On an integral equation for the free-boundary of stochastic, irreversible investment problems. <em>The Annals of Applied Probability</em> 25, 150-176.
Ferrari, G.: On an integral equation for the free-boundary of stochastic, irreversible investment problems. The Annals of Applied Probability. 25, 150-176 (2015).
27189952015-02-16T10:39:54Z2018-07-24T13:01:24Z