TY  - GEN
AB  - 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.
DA  - 2014
KW  - free-boundary
KW  - irreversible investment
KW  - singular stochastic control
KW  - optimal stopping
KW  - Lévy process
KW  - Bank and El Karoui's representation theorem
KW  - base capacity
LA  - eng
PY  - 2014
SN  - 0931-6558
SP  - 20-
TI  - Irreversible Investment under Lévy Uncertainty: an Equation for the Optimal Boundary
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-29016857
Y2  - 2024-11-22T13:43:57
ER  -