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

Ferrari G, Salminen P (2014) Center for Mathematical Economics Working Papers; 530.
Bielefeld: Center for Mathematical Economics.

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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.
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Ferrari G, Salminen P. Irreversible Investment under Lévy Uncertainty: an Equation for the Optimal Boundary. Center for Mathematical Economics Working Papers. Vol 530. Bielefeld: Center for Mathematical Economics; 2014.
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.
Ferrari, G., and 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.
Ferrari, G., & Salminen, P., 2014. Irreversible Investment under Lévy Uncertainty: an Equation for the Optimal Boundary, Center for Mathematical Economics Working Papers, no.530, Bielefeld: Center for Mathematical Economics.
G. Ferrari and P. Salminen, Irreversible Investment under Lévy Uncertainty: an Equation for the Optimal Boundary, Center for Mathematical Economics Working Papers, vol. 530, Bielefeld: Center for Mathematical Economics, 2014.
Ferrari, G., Salminen, P.: Irreversible Investment under Lévy Uncertainty: an Equation for the Optimal Boundary. Center for Mathematical Economics Working Papers, 530. Center for Mathematical Economics, Bielefeld (2014).
Ferrari, Giorgio, and Salminen, Paavo. Irreversible Investment under Lévy Uncertainty: an Equation for the Optimal Boundary. Bielefeld: Center for Mathematical Economics, 2014. Center for Mathematical Economics Working Papers. 530.
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