American options with lookback payoff

We examine the early exercise policies and pricing behaviors of one-asset American options with lookback payoff structures. The classes of option models considered include floating strike lookback options, Russian options, fixed strike lookback options, and the pricing model of the dynamic protection fund. For each class of the American lookback options, we analyze the optimal stopping region, in particular the asymptotic behavior at times close to expiration and at infinite time to expiration. The interrelations between the price functions of these American lookback options are explored. The mathematical technique of analyzing the exercise boundary curves of lookback options at infinitesimally small asset values is also applied to the American two-asset minimum put option model.