An integral equation approach for optimal investment policies with partial reversibility. (August 2019) - Jeon, Junkee; Kim, Geonwoo
Highlights: We deal with an irreversible investment with partially reversibility. Mellin transforms are used to derive the integral equation for the optimal investment. We use recursive integration method to obtain the optimal investment boundary and the disinvestment boundary. Abstract: In this paper we investigate an investment problem with partial reversibility proposed by Abel and Eberly [4] in a finite horizon. In this model, a firm can purchase capital at a given price and sell capital at a lower price. This problem can be categorized into a singular control problem and can be formulated as a Hamilton–Jacobi–Bellman(HJB) equation. Based on theoretical results in [10] and the Mellin transform techniques, we derive the coupled integral equations satisfied by the optimal investment and disinvestment boundaries, respectively. By using the recursive integration method, we solve numerically the integral equations and present the optimal investment boundary and disinvestment boundary.