Abstract
This paper studies an irreversible investment problem under a finite horizon. The firm expands its production capacity in irreversible investments by purchasing capital to increase productivity. This problem is a singular stochastic control problem and its associated Hamilton–Jacobi–Bellman equation is derived. By using a Mellin transform, we obtain the integral equation satisfied by the free boundary of this investment problem. Furthermore, we solve the integral equation numerically using the recursive integration method and present the graph for the free boundary.
Highlights
In economics, optimal investment problems have received much attention over the last few decades
Dangl [4] investigated an irreversible investment problem when a firm decides on optimal investment timing and optimal capacity choice at the same time under the condition of uncertainty demand
Mathematics 2020, 8, 2084 of double Mellin transforms are used appropriately to obtain the integral equation for the optimal investment with a finite horizon
Summary
Optimal investment problems have received much attention over the last few decades. The main contribution of this paper is an efficient derivation of the integral equation for an irreversible investment problem using Mellin transforms. We employ the partial differential equation (PDE) approach to solve the problem and derive the integral equation for the free boundary of the investment problem using Mellin transforms. We adopt a Mellin transform approach to derive the integral equation for irreversible optimal investment with a finite horizon. Mathematics 2020, 8, 2084 of double Mellin transforms are used appropriately to obtain the integral equation for the optimal investment with a finite horizon. This approach induces the integral equation more efficiently.
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