IRREVERSIBLE INVESTMENT UNDER LEVY UNCERTAINTY: AN EQUATION FOR THE OPTIMAL BOUNDARY
Ferrari, Giorgio
Salminen, Paavo
Free-boundary
irreversible investment
singular stochastic control
optimal stopping
Levy process
Bank and El Karoui's representation
theorem
base capacity
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.
Applied Probability Trust
2016
info:eu-repo/semantics/article
doc-type:article
text
https://pub.uni-bielefeld.de/record/2906562
Ferrari G, Salminen P. IRREVERSIBLE INVESTMENT UNDER LEVY UNCERTAINTY: AN EQUATION FOR THE OPTIMAL BOUNDARY. <em>ADVANCES IN APPLIED PROBABILITY</em>. 2016;48(1):298-314.
eng
info:eu-repo/semantics/altIdentifier/doi/10.1017/apr.2015.18
info:eu-repo/semantics/altIdentifier/issn/0001-8678
info:eu-repo/semantics/altIdentifier/issn/1475-6064
info:eu-repo/semantics/altIdentifier/wos/000384819200016
info:eu-repo/semantics/closedAccess