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On the Continuous and Smooth Fit Principle for Optimal Stopping Problems in Spectrally Negative Lévy Models

  • Masahiko Egami (a1) and Kazutoshi Yamazaki (a2)

We consider a class of infinite time horizon optimal stopping problems for spectrally negative Lévy processes. Focusing on strategies of threshold type, we write explicit expressions for the corresponding expected payoff via the scale function, and further pursue optimal candidate threshold levels. We obtain and show the equivalence of the continuous/smooth fit condition and the first-order condition for maximization over threshold levels. As examples of its applications, we give a short proof of the McKean optimal stopping problem (perpetual American put option) and solve an extension to Egami and Yamazaki (2013).

Corresponding author
Postal address: Graduate School of Economics, Kyoto University, Sakyo-Ku, Kyoto, 606-8501, Japan. Email address:
∗∗ Postal address: Department of Mathematics, Faculty of Engineering Science, Kansai University, Suita-shi, Osaka, 564-8680, Japan. Email address:
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Advances in Applied Probability
  • ISSN: 0001-8678
  • EISSN: 1475-6064
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