Optimal Stopping and Convergence for Americal Type Options

Lecture presents a survey of results from a new book with an above title,
being at the moment in the final stage of preparation.  The book is
devoted to approximation methods for option rewards of American type
options for multivariate modulatd Markov type price processes with
discrete time.  The classes of price processes under consideration include
multivariate modulated Markov chains, modulated random walks, and various
autoregressive models of price processes.  General convergence results are
presented, as well as their applications to space skeleton approximations
and tree approximation algorithms. Also, results related to studies of
structure for optimal stopping domains are presented as well as results
related to option reselling problem. Theoretical results are illustrated
by results of experimental studies.  Finally, connection with problems of
optimal stopping and convergence for multivariate modulatd Markov type
price processes with continuous time is discussed.