Sammanfattning
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, weshow that the optimal boundary is intimately linked to the uniqueoptional solution of an appropriate Bank-El Karoui representationproblem. Such a relation and the Wiener-Hopf factorization allow us toderive an integral equation for the optimal investmentboundary. In case the underlying Lévy process hits any point in $ \RR$ 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 thefunction is separable and in the second case non-separable.\smallskip
Originalspråk | Odefinierat/okänt |
---|---|
Sidor (från-till) | 298–314 |
Tidskrift | Advances in Applied Probability |
Volym | 48 |
Nummer | 1 |
DOI | |
Status | Publicerad - 2016 |
MoE-publikationstyp | A1 Tidskriftsartikel-refererad |