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2019 Optimal stopping of oscillating Brownian motion
Ernesto Mordecki, Paavo Salminen
Electron. Commun. Probab. 24: 1-12 (2019). DOI: 10.1214/19-ECP250

Abstract

We solve optimal stopping problems for an oscillating Brownian motion, i.e. a diffusion with positive piecewise constant volatility changing at the point $x=0$. Let $\sigma _{1}$ and $\sigma _{2}$ denote the volatilities on the negative and positive half-lines, respectively. Our main result is that continuation region of the optimal stopping problem with reward $((1+x)^{+})^{2}$ can be disconnected for some values of the discount rate when $2\sigma _{1}^{2}<\sigma _{2}^{2}$. Based on the fact that the skew Brownian motion in natural scale is an oscillating Brownian motion, the obtained results are translated into corresponding results for the skew Brownian motion.

Citation

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Ernesto Mordecki. Paavo Salminen. "Optimal stopping of oscillating Brownian motion." Electron. Commun. Probab. 24 1 - 12, 2019. https://doi.org/10.1214/19-ECP250

Information

Received: 4 March 2019; Accepted: 19 June 2019; Published: 2019
First available in Project Euclid: 12 September 2019

zbMATH: 1422.60134
MathSciNet: MR4003124
Digital Object Identifier: 10.1214/19-ECP250

Subjects:
Primary: 60J60, 60J65, 62L15

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