1. Main Goals The theory of asset pricing has grown markedly more sophisticated in the last two decades, with the application of powerful mathematical tools such as probability theory, shastic processes and numerical analysis. The main goal of this book is to provide a systematic exposition, with practical applications, of the no-arbitrage theory for asset pricing in financial engineering in the framework of a discrete time approach. The book should also serve well as a textbook on financial asset pricing. It should be accessible to a broad audi­ ence, in particular to practitioners in financial and related industries, as well as to students in MBA or graduate/advanced undergraduate programs in finance, financial engineering, financial econometrics, or financial information science. The no-arbitrage asset pricing theory is based on the simple and well ac­ cepted principle that financial asset prices are instantly adjusted at each mo­ ment in time in order not to allow an arbitrage opportunity. Here an arbitrage opportunity is an opportunity to have a portfolio of value aat an initial time lead to a positive terminal value with probability 1 (equivalently, at no risk), with money neither added nor subtracted from the portfolio in rebalancing dur­ ing the investment period. It is necessary for a portfolio of valueato include a short-sell position as well as a long-buy position of some assets.