Irreversible investment under Lévy uncertainty: an equation for the optimal boundary

A1 Journal article (refereed)


Internal Authors/Editors


Publication Details

List of Authors: Giorgio Ferrari, Paavo Salminen
Publisher: Probability Trust
Publication year: 2016
Journal: Advances in Applied Probability
Volume number: 48
Issue number: 1
Start page: 298
End page: 314


Abstract

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 $ \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 the
function is separable and in the second case non-separable.
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Last updated on 2020-28-05 at 01:28