Ferrari, G. & Salminen, P. (2014). *Irreversible Investment under Lévy Uncertainty: an Equation for the Optimal Boundary* (Center for Mathematical Economics Working Papers). Bielefeld: Center for Mathematical Economics.

","aps":" G. Ferrari and P. Salminen, Irreversible Investment under Lévy Uncertainty: an Equation for the Optimal Boundary, Center for Mathematical Economics Working Papers (Center for Mathematical Economics, Bielefeld, 2014).","chicago":"Ferrari, Giorgio, and Salminen, Paavo. 2014. *Irreversible Investment under Lévy Uncertainty: an Equation for the Optimal Boundary*. Vol. 530. Center for Mathematical Economics Working Papers. Bielefeld: Center for Mathematical Economics.

","ieee":" G. Ferrari and P. Salminen, Bielefeld: Center for Mathematical Economics.","wels":"Ferrari, G.; Salminen, P. (2014): Irreversible Investment under Lévy Uncertainty: an Equation for the Optimal Boundary. Bielefeld: Center for Mathematical Economics.","mla":"Ferrari, Giorgio, and Salminen, Paavo.

Bielefeld: Center for Mathematical Economics.","frontiers":"Ferrari, G., and Salminen, P. (2014). Irreversible Investment under Lévy Uncertainty: an Equation for the Optimal Boundary.

Ferrari, G., & Salminen, P. (2014). *Irreversible Investment under Lévy Uncertainty: an Equation for the Optimal Boundary* (Center for Mathematical Economics Working Papers, 530). Bielefeld: Center for Mathematical Economics.

"},"publication_identifier":{"issn":["0931-6558"]},"abstract":[{"text":"We derive a new equation for the optimal investment boundary of a general\r\nirreversible investment problem under exponential Lévy uncertainty. The problem is set as an\r\ninfinite time-horizon, two-dimensional degenerate singular stochastic control problem. In line\r\nwith the results recently obtained in a diffusive setting, we show that the optimal boundary is intimately\r\nlinked to the unique optional solution of an appropriate Bank-El Karoui representation\r\nproblem. Such a relation and the Wiener-Hopf factorization allow us to derive an integral equation\r\nfor the optimal investment boundary. In case the underlying Lévy process hits any point\r\nin R with positive probability we show that the integral equation for the investment boundary\r\nis uniquely satisfied by the unique solution of another equation which is easier to handle. As a\r\nremarkable by-product we prove the continuity of the optimal investment boundary. The paper\r\nis concluded with explicit results for profit functions of (i) Cobb-Douglas type and (ii) CES type.\r\nIn the first case the function is separable and in the second case non-separable.","lang":"eng"}],"title":"Irreversible Investment under Lévy Uncertainty: an Equation for the Optimal Boundary","file_date_updated":"2019-09-06T09:18:36Z","jel":["C02","E22","D92","G31"],"date_updated":"2018-07-24T13:00:59Z","publication_status":"published","series_title":"Center for Mathematical Economics Working Papers","language":[{"iso":"eng"}],"urn":"urn:nbn:de:0070-pub-29016857","oa":1,"locked":"1","keyword":["free-boundary","irreversible investment","singular stochastic control","optimal stopping","Lévy process","Bank and El Karoui's representation theorem","base capacity"],"department":[{"_id":"10053"}],"has_accepted_license":"1","place":"Bielefeld","status":"public","ddc":["330"],"publisher":"Center for Mathematical Economics","author":[{"full_name":"Ferrari, Giorgio","first_name":"Giorgio","last_name":"Ferrari","id":"32701753"},{"full_name":"Salminen, Paavo","last_name":"Salminen","first_name":"Paavo"}],"page":"20","file":[{"file_size":"376849","access_level":"open_access","file_name":"IMW_working_paper_530.pdf","date_created":"2016-03-16T10:03:16Z","file_id":"2901686","relation":"main_file","date_updated":"2019-09-06T09:18:36Z","content_type":"application/x-download","creator":"weingarten"}],"_id":"2901685","intvolume":" 530","volume":530,"date_created":"2016-03-16T10:07:38Z"}]