This book is devoted to the mathematical studies of stochastic systems with quasi-stationary phenomena which have applications to population dynamics or epidemic models. In addition to its use for the research and reference purposes, the book can also be used in special courses on the subject and as a complementary reading in general courses on stochastic processes. In this respect, it may be useful for specialists as well as doctoral and advanced undergraduate students.

This book gives a systematical presentation of stochastic approximation methods for models of American-type options with general pay-off functions for discrete time Markov price processes. It is the first volume of the comprehensive two volumes monograph.

The second volume of this systematical presentation of stochastic approximation methods for models of American-type options presents results on structural studies of optimal stopping domains, Monte Carlo based approximation reward algorithms, and convergence of American-type options for autoregressive and continuous time models, as well as results of the corresponding experimental studies.