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

Haoyan Zhang () and Yingxu Tian ()
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Haoyan Zhang: Civil Aviation University of China
Yingxu Tian: Civil Aviation University of China

Methodology and Computing in Applied Probability, 2022, vol. 24, issue 2, 1237-1251

Abstract: 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.

Keywords: Sticky brownian motion; First hitting time; Optimal stopping; Bond pricing (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11009-021-09923-0

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