Dmitrii Silvestrov: American-type Options. Stochastic Approximation Methods

The lecture presents a survey of results from my new book [1], which is devoted to stochastic approximation methods for rewards of American type options for multivariate modulated Markov log-price processes. The classes of discrete and continuous time log-price processes (LPP) under consideration include multivariate modulated Markov chains, modulated random walks, and various autoregressive models, multivariate modulated Markov log-price processes, diffusion and Lévy processes. General convergence results are presented, as well as their applications to space skeleton approximations, tree approximations, and Monte Carlo based approximation algorithms for option rewards. 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. The book contains two parts and the lecture will be mainly concentrated on the results related to discrete time processes.

References

[1] Silvestrov D.S. American-type Options. Stochastic Approximation Methods. Volume I. De Gruyter Studies in Mathematics 56, De Gruyter, 2014, X + 509 pages