An Integral Equation Approach to the Irreversible Investment Problem with a Finite Horizon

Junkee Jeon and Geonwoo Kim
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Junkee Jeon: Department of Applied Mathematics & Institute of Natural Science, Kyung Hee University, Seoul 01811, Korea
Geonwoo Kim: School of Liberal Arts, Seoul National University of Science and Technology, Seoul 01811, Korea

Mathematics, 2020, vol. 8, issue 11, 1-10

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.

Keywords: investment problem; free boundary; Mellin transform; integral equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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