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Hitting Time Problems of Sticky Brownian Motion and Their Applications in Optimal Stopping and Bond Pricing

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  • Haoyan Zhang

    (Civil Aviation University of China)

  • Yingxu Tian

    (Civil Aviation University of China)

Abstract

This paper investigates the hitting time problems of sticky Brownian motion and their applications in optimal stopping and bond pricing. We study the Laplace transform of first hitting time over the constant and random jump boundary, respectively. The results about hitting the constant boundary serve for solving the optimal stopping problem of sticky Brownian motion. By introducing the sharpo ratio, we settle the bond pricing problem under sticky Brownian motion as well. An interesting result shows that the sticky point is in the continuation region and all the results we get are in closed form.

Suggested Citation

  • Haoyan Zhang & Yingxu Tian, 2022. "Hitting Time Problems of Sticky Brownian Motion and Their Applications in Optimal Stopping and Bond Pricing," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 1237-1251, June.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:2:d:10.1007_s11009-021-09923-0
    DOI: 10.1007/s11009-021-09923-0
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    References listed on IDEAS

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    1. Luis H. R. Alvarez E. & Paavo Salminen, 2017. "Timing in the presence of directional predictability: optimal stopping of skew Brownian motion," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(2), pages 377-400, October.
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