Irreversible Investment under Lévy Uncertainty: an Equation for the Optimal Boundary

Giorgio Ferrari and Paavo Salminen
Additional contact information
Giorgio Ferrari: Center for Mathematical Economics, Bielefeld University
Paavo Salminen: Center for Mathematical Economics, Bielefeld University

No 530, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

Abstract: We derive a new equation for the optimal investment boundary of a general irreversible investment problem under exponential Lévy 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 Lévy 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 (i) Cobb-Douglas type and (ii) CES type. In the first case the function is separable and in the second case non-separable.

Keywords: free-boundary; irreversible investment; singular stochastic control; optimal stopping; Lévy process; Bank and El Karoui's representation theorem; base capacity (search for similar items in EconPapers)
Pages: 20
Date: 2016-03-16
New Economics Papers: this item is included in nep-mac
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
https://pub.uni-bielefeld.de/download/2901685/2901686 First Version, 2014 (application/x-download)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bie:wpaper:530

Access Statistics for this paper

More papers in Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University Contact information at EDIRC.
Bibliographic data for series maintained by Bettina Weingarten ().