Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/111065
Authors: 
Ferrari, Giorgio
Salminen, Paavo
Year of Publication: 
2014
Series/Report no.: 
Working Papers, Center for Mathematical Economics 530
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.
Subjects: 
free-boundary
irreversible investment
singular stochastic control
optimal stopping
Lévy process
Bank and El Karoui's representation theorem
base capacity
JEL: 
C02
E22
D92
G31
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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