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http://hdl.handle.net/10397/93897
Title: | Optimal redeeming strategy of stock loans under drift uncertainty | Authors: | Xu, ZQ Yi, F |
Issue Date: | Feb-2020 | Source: | Mathematics of operations research, Feb. 2020, v. 45, no. 1, p. 384-401 | Abstract: | In practice, one must recognize the inevitable incompleteness of information while making decisions. In this paper, we consider the optimal redeeming problem of stock loans under a state of incomplete information presented by the uncertainty in the (bull or bear) trends of the underlying stock. This is called drift uncertainty. Owing to the unavoidable need for the estimation of trends while making decisions, the related Hamilton–Jacobi–Bellman equation turns out to be of a degenerate parabolic type. Hence, it is very hard to obtain its regularity using the standard approach, making the problem different from the existing optimal redeeming problems without drift uncertainty. We present a thorough and delicate probabilistic and functional analysis to obtain the regularity of the value function and the optimal redeeming strategies. The optimal redeeming strategies of stock loans appear significantly different in the bull and bear trends. | Keywords: | Bull and bear trends Degenerate parabolic variational inequality Drift uncertainty Optimal stopping Stock loan |
Publisher: | Institute for Operations Research and the Management Sciences | Journal: | Mathematics of operations research | ISSN: | 0364-765X | EISSN: | 1526-5471 | DOI: | 10.1287/MOOR.2019.0995 | Rights: | Copyright:© 2019 INFORMS This is the accepted manuscript of the following article: Xu, Z. Q., & Yi, F. (2020). Optimal redeeming strategy of stock loans under drift uncertainty. Mathematics of Operations Research, 45(1), 384-401, which has been published in final form at https://doi.org/10.1287/MOOR.2019.0995 |
Appears in Collections: | Journal/Magazine Article |
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Xu_Optimal_Redeeming_Strategy.pdf | Pre-Published version | 1.11 MB | Adobe PDF | View/Open |
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