@article{2906562,
abstract = {We derive a new equation for the optimal investment boundary of a general irreversible investment problem under exponential Levy uncertainty. The problem is set as an infinite time-horizon, two-dimensional degenerate singular stochastic control problem. In line with the results recently obtained in a diffusive setting, we show that the optimal boundary is intimately linked to the unique optional solution of an appropriate Bank-El Karoui representation problem. Such a relation and the Wiener-Hopf factorization allow us to derive an integral equation for the optimal investment boundary. In case the underlying Levy process hits any point in R with positive probability we show that the integral equation for the investment boundary is uniquely satisfied by the unique solution of another equation which is easier to handle. As a remarkable by-product we prove the continuity of the optimal investment boundary. The paper is concluded with explicit results for profit functions of Cobb-Douglas type and CES type. In the former case the function is separable and in the latter case nonseparable.},
author = {Ferrari, Giorgio and Salminen, Paavo},
issn = {1475-6064},
journal = {ADVANCES IN APPLIED PROBABILITY},
number = {1},
pages = {298--314},
publisher = {Applied Probability Trust},
title = {{IRREVERSIBLE INVESTMENT UNDER LEVY UNCERTAINTY: AN EQUATION FOR THE OPTIMAL BOUNDARY}},
doi = {10.1017/apr.2015.18},
volume = {48},
year = {2016},
}