On the continuous and smooth fit principle for optimal stopping problems in spectrally negative levy models. Adv

ABSTRACT. This paper is concerned with 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. This together with problem-specific information about the payoff function can prove optimality over all stopping times. As examples, we give an alternative proof for the perpetual American option pricing problem and solve an extension to Egami and Yamazaki [17]