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http://hdl.handle.net/10397/93822
Title: | Free boundary problem for an optimal investment problem with a borrowing constraint | Authors: | Guan, C Li, X Zhou, R Zhou, W |
Issue Date: | May-2022 | Source: | Journal of industrial and management optimization, May 2022, v. 18, no. 3, p. 1915-1934 | Abstract: | This paper considers an optimal investment problem under CRRA utility with a borrowing constraint. We formulate it into a free boundary problem consisting of a fully nonlinear equation and a linear equation. We prove the existence and uniqueness of the classical solution and present the condition for the existence of the free boundary under a linear constraint on a borrowing rate. Furthermore, we prove that the free boundary is continuous and smooth when the relative risk aversion coefficient is sufficiently small. | Keywords: | Borrowing constraint CRRA utility Free boundary problem Optimal investment Stochastic optimal control |
Publisher: | American Institute of Mathematical Sciences | Journal: | Journal of industrial and management optimization | ISSN: | 1553-166X | EISSN: | 1547-5816 | DOI: | 10.3934/jimo.2021049 | Rights: | This is an Open Access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). The following publication Guan, C., Li, X., Zhou, R., & Zhou, W. (2022). Free boundary problem for an optimal investment problem with a borrowing constraint. Journal of Industrial and Management Optimization, 18(3), 1915 is available at https://doi.org/10.3934/jimo.2021049. |
Appears in Collections: | Journal/Magazine Article |
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