The smooth-fit property in an exponential Lévy model

Damien Lamberton (1, 2) , Mohammed Mikou (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 MATHRISK - Mathematical Risk handling

We study the smooth-fit property of the American put price with finite maturity in an exponential Lévy model when the underlying stock pays dividends at a continuous rate. As in the perpetual case, a regularity property is sufficient for smooth-fit to occur. We also derive conditions on the Lévy measure under which smooth-fit fails.

Mots clés: Optimal stopping; Lévy processes; smooth-fit property; American options.; American options

Domaines: Probabilités [math.PR]

Damien Lamberton, Mohammed Mikou. The smooth-fit property in an exponential Lévy model. Journal of Applied Probability, 2012, 49 (1), pp.137-149. ⟨hal-00677327⟩