Ferrari, Giorgio
Giorgio
Ferrari
Salminen, Paavo
Paavo
Salminen
Irreversible Investment under Lévy Uncertainty: an Equation for the Optimal Boundary
Center for Mathematical Economics
2014
2016-03-16T10:07:38Z
2018-07-24T13:00:59Z
working_paper
https://pub.uni-bielefeld.de/record/2901685
https://pub.uni-bielefeld.de/record/2901685.json
0931-6558
urn:nbn:de:0070-pub-29016857
376849 bytes
application/x-download
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.