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.

","mla":"Ferrari, Giorgio. “On an integral equation for the free-boundary of stochastic, irreversible investment problems”. 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

","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.

","ieee":" G. Ferrari, “On an integral equation for the free-boundary of stochastic, irreversible investment problems”, On an integral equation for the free-boundary of stochastic, irreversible investment problems.

The Annals of Applied Probability 25(1): 150-176."},"additionalInformation":"ISI import, vp","volume":"25","title":"On an integral equation for the free-boundary of stochastic, irreversible investment problems","intvolume":" 25","keyword":["and El Karoui's representation theorem","one-dimensional diffusion","Bank","optimal stopping","stochastic control","singular","irreversible investment","free-boundary","Integral equation","base capacity"],"accept":"1","publication_status":"published","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."}],"year":"2015","status":"public","publisher":"Institute Of Mathematical Statistics","doi":"10.1214/13-AAP991","date_created":"2015-02-16T10:39:54Z","date_submitted":"2015-02-16T12:25:11Z","issue":"1"}]