This book contains mostly the author's up-to-date research results in
the area. Option pricing has attracted much attention in the past decade
from applied mathematicians, statisticians, practitioners and educators.
Many partial differential equation-based theoretical models have been
developed for valuing various options. These models do not have any
practical use unless their solutions can be found. However, most of
these models are far too complex to solve analytically and numerical
approximations have to be sought in practice.
The contents of the book consist of three parts: (i) basic theory of
stochastic control and formulation of various option pricing models,
(ii) design of finite volume, finite difference and penalty-based
algorithms for solving the models and (iii) stability and convergence
analysis of the algorithms. It also contains extensive numerical
experiments demonstrating how these algorithms perform for practical
problems. The theoretical and numerical results demonstrate these
algorithms provide efficient, accurate and easy-to-implement numerical
tools for financial engineers to price options.
This book is appealing to researchers in financial engineering, optimal
control and operations research. Financial engineers and practitioners
will also find the book helpful in practice.