Optimal Stopping and Convergence of Option Rewards

Abstract: This thesis is based on two articles devoted to optimal stopping problems of American type options.In article A, we study the problem of optimal reselling for European options. The problem can be transformed to the problem of exercising an American option with two underlying. An approximate binomial-trinomial tree algorithm for the reselling model is constructed.In article B, we get general convergence results for the American option rewards for multivariate Markov price processes. These results are used to prove convergence of tree approximations presented in papers A and B.