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

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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)

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.

Suggested Citation

  • Junkee Jeon & Geonwoo Kim, 2020. "An Integral Equation Approach to the Irreversible Investment Problem with a Finite Horizon," Mathematics, MDPI, vol. 8(11), pages 1-10, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:2084-:d:449124
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    References listed on IDEAS

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