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Mathematics
Volume 8
Issue 11
10.3390/math8112084
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Article

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

by
Junkee Jeon
1 and
Geonwoo Kim
2,*
1
Department of Applied Mathematics & Institute of Natural Science, Kyung Hee University, Seoul 01811, Korea
2
School of Liberal Arts, Seoul National University of Science and Technology, Seoul 01811, Korea
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(11), 2084; https://doi.org/10.3390/math8112084
Submission received: 6 November 2020 / Revised: 19 November 2020 / Accepted: 20 November 2020 / Published: 22 November 2020
(This article belongs to the Special Issue Application of Mathematical Analysis and Models to Financial Economics)
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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 investment problem; free boundary; Mellin transform; integral equation

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MDPI and ACS Style

Jeon, J.; Kim, G. An Integral Equation Approach to the Irreversible Investment Problem with a Finite Horizon. Mathematics 2020, 8, 2084. https://doi.org/10.3390/math8112084

AMA Style

Jeon J, Kim G. An Integral Equation Approach to the Irreversible Investment Problem with a Finite Horizon. Mathematics. 2020; 8(11):2084. https://doi.org/10.3390/math8112084

Chicago/Turabian Style

Jeon, Junkee, and Geonwoo Kim. 2020. "An Integral Equation Approach to the Irreversible Investment Problem with a Finite Horizon" Mathematics 8, no. 11: 2084. https://doi.org/10.3390/math8112084

APA Style

Jeon, J., & Kim, G. (2020). An Integral Equation Approach to the Irreversible Investment Problem with a Finite Horizon. Mathematics, 8(11), 2084. https://doi.org/10.3390/math8112084

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