Moroz A. Optimal stopping problem in Levy model

The thesis is devoted to the optimal stopping problem in Levy models for American type contingent claims.The properties of value functions in Levy model are studied. It is shown that for the put option in Levy models the optimal stopping time is the first time when the price process reaches a certain level. The behavior of value function is studied, when the maturity diverges to infinity. Sufficient conditions for non-emptiness and for threshold structure of optimal stopping region are provided. For solutions stochastic differential equations with jumps a convergence result is established and it is proved that the hitting times of certain sets converge as well.