IRREVERSIBLE INVESTMENT UNDER LEVY UNCERTAINTY: AN EQUATION FOR THE OPTIMAL BOUNDARY

Ferrari G, Salminen P (2016)
ADVANCES IN APPLIED PROBABILITY 48(1): 298-314.

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We derive a new equation for the optimal investment boundary of a general irreversible investment problem under exponential Levy 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 Levy 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.
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Ferrari G, Salminen P. IRREVERSIBLE INVESTMENT UNDER LEVY UNCERTAINTY: AN EQUATION FOR THE OPTIMAL BOUNDARY. ADVANCES IN APPLIED PROBABILITY. 2016;48(1):298-314.
Ferrari, G., & Salminen, P. (2016). IRREVERSIBLE INVESTMENT UNDER LEVY UNCERTAINTY: AN EQUATION FOR THE OPTIMAL BOUNDARY. ADVANCES IN APPLIED PROBABILITY, 48(1), 298-314.
Ferrari, G., and Salminen, P. (2016). IRREVERSIBLE INVESTMENT UNDER LEVY UNCERTAINTY: AN EQUATION FOR THE OPTIMAL BOUNDARY. ADVANCES IN APPLIED PROBABILITY 48, 298-314.
Ferrari, G., & Salminen, P., 2016. IRREVERSIBLE INVESTMENT UNDER LEVY UNCERTAINTY: AN EQUATION FOR THE OPTIMAL BOUNDARY. ADVANCES IN APPLIED PROBABILITY, 48(1), p 298-314.
G. Ferrari and P. Salminen, “IRREVERSIBLE INVESTMENT UNDER LEVY UNCERTAINTY: AN EQUATION FOR THE OPTIMAL BOUNDARY”, ADVANCES IN APPLIED PROBABILITY, vol. 48, 2016, pp. 298-314.
Ferrari, G., Salminen, P.: IRREVERSIBLE INVESTMENT UNDER LEVY UNCERTAINTY: AN EQUATION FOR THE OPTIMAL BOUNDARY. ADVANCES IN APPLIED PROBABILITY. 48, 298-314 (2016).
Ferrari, Giorgio, and Salminen, Paavo. “IRREVERSIBLE INVESTMENT UNDER LEVY UNCERTAINTY: AN EQUATION FOR THE OPTIMAL BOUNDARY”. ADVANCES IN APPLIED PROBABILITY 48.1 (2016): 298-314.
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