### Abstract

Novikov and Shiryaev (2004) give explicit solutions to a class of optimal stopping problems for random walks based on other similar examples given in Darling et al. (1972). We give the analogue of their results when the random walk is replaced by a Lévy process. Further we show that the solutions show no contradiction with the conjecture given in Alili and Kyprianou (2004) that there is smooth pasting at the optimal boundary if and only if the boundary of the stopping reigion is irregular for the interior of the stopping region.

Original language | English |
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Journal | Electronic Communications in Probability |

Volume | 10 |

Publication status | Published - 2005 |

### Keywords

- Appell polynomials
- Lévy processes
- Optimal stopping problem
- Pasting principles

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## Cite this

Kyprianou, A. E., & Surya, B. A. (2005). On the novikov-shiryaev optimal stopping problems in continuous time.

*Electronic Communications in Probability*,*10*.