Stopping Levels for a Spectrally Negative Markov Additive Process
COMMUNICATIONS IN MATHEMATICS AND STATISTICS, cilt.14, sa.2, ss.369-390, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 14 Sayı: 2
- Basım Tarihi: 2026
- Doi Numarası: 10.1007/s40304-023-00385-z
- Dergi Adı: COMMUNICATIONS IN MATHEMATICS AND STATISTICS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.369-390
- Orta Doğu Teknik Üniversitesi Adresli: Evet
Özet
The optimal stopping problem for pricing Russian options in finance requires taking the supremum of the discounted reward function over all finite stopping times. We assume the logarithm of the asset price is a spectrally negative Markov additive process with finitely many regimes. The reward function is given by the exponential of the running supremum of the price process. Previous work on Russian optimal stopping problem suggests that the optimal stopping time would be an upcrossing time of the drawdown at a certain level for each regime. We derive explicit formulas for identifying the stopping levels and computing the corresponding value functions through a recursive algorithm. A numerical is provided for finding these stopping levels and their value functions.