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Optimal Redeeming Strategy of Stock Loans Under Drift Uncertainty

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  • Zuo Quan Xu

    (Department of Applied Mathematics, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong;)

  • Fahuai Yi

    (School of Mathematics and Statistics, Guangdong University of Foreign Studies, Guangzhou, 510006 Guangdong, China)

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.

Suggested Citation

  • Zuo Quan Xu & Fahuai Yi, 2020. "Optimal Redeeming Strategy of Stock Loans Under Drift Uncertainty," Mathematics of Operations Research, INFORMS, vol. 45(1), pages 384-401, February.
    • Handle: RePEc:inm:ormoor:v:45:y:2020:i:1:p:384-401
    DOI: 10.1287/moor.2019.0995
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    References listed on IDEAS

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    1. Zuo Quan Xu, 2016. "A Note On The Quantile Formulation," Mathematical Finance, Wiley Blackwell, vol. 26(3), pages 589-601, July.
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    7. Zuo Quan Xu & Xun Yu Zhou, 2011. "Optimal stopping under probability distortion," Papers 1103.1755, arXiv.org, revised Feb 2013.
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    Cited by:

    1. Xing, Jie & Ma, Jingtang & Yang, Wensheng, 2023. "Optimal entry decision of unemployment insurance under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 110(C), pages 31-52.

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