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March 2016 Irreversible investment under Lévy uncertainty: an equation for the optimal boundary
Giorgio Ferrari, Paavo Salminen
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Adv. in Appl. Probab. 48(1): 298-314 (March 2016).

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 Cobb-Douglas type and CES type. In the former case the function is separable and in the latter case nonseparable.

Citation

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Giorgio Ferrari. Paavo Salminen. "Irreversible investment under Lévy uncertainty: an equation for the optimal boundary." Adv. in Appl. Probab. 48 (1) 298 - 314, March 2016.

Information

Published: March 2016
First available in Project Euclid: 8 March 2016

zbMATH: 1341.93108
MathSciNet: MR3473579

Subjects:
Primary: 93E20
Secondary: 60G40, 60G51, 91B70

Rights: Copyright © 2016 Applied Probability Trust

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Vol.48 • No. 1 • March 2016
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