Optimal stopping of oscillating Brownian motion
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 σ1 and σ 2 denote the volatilities on the negative and positive half-lines, respectively. Our main result is that continuation region of...
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| Médium: | article |
| Jazyk: | angličtina |
| Vydáno: |
2019
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| On-line přístup: | https://hdl.handle.net/20.500.12008/28109 |
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| Shrnutí: | 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 σ1 and σ 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 σ 21 <σ22. 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. |
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