In this edition two new chapters, 9 and 10, on mathematical finance are<br/>added. They are written by Dr. Farid AitSahlia, ancien &acute;el`eve, who has<br/>taught such a course and worked on the research staff of several industrial<br/>and financial institutions.<br/>The new text begins with a meticulous account of the uncommon vocabulary<br/>and syntax of the financial world; its manifold options and actions,<br/>with consequent expectations and variations, in the marketplace. These are<br/>then expounded in clear, precise mathematical terms and treated by the<br/>methods of probability developed in the earlier chapters. Numerous graded<br/>and motivated examples and exercises are supplied to illustrate the applicability<br/>of the fundamental concepts and techniques to concrete financial<br/>problems. For the reader whose main interest is in finance, only a portion<br/>of the first eight chapters is a “prerequisite” for the study of the last two<br/>chapters. Further specific references may be scanned from the topics listed<br/>in the Index, then pursued in more detail.<br/>I have taken this opportunity to fill a gap in Section 8.1 and to expand<br/>Appendix 3 to include a useful proposition on martingale stopped at an<br/>optional time. The latter notion plays a basic role in more advanced financial<br/>and other disciplines. However, the level of our compendium remains<br/>elementary, as befitting the title and scheme of this textbook. We have also<br/>included some up-to-date financial episodes to enliven, for the beginners,<br/>the stratified atmosphere of “strictly business”. We are indebted to Ruth<br/>Williams, who read a draft of the new chapters with valuable suggestions<br/>for improvement; to Bernard Bru and Marc Barbut for information on the<br/>Pareto-L&acute;evy laws originally designed for income distributions. It is hoped<br/>that a readable summary of this renowned work may be found in the new<br/>Appendix 4.<br/>Kai Lai Chung<br/>August 3, 2002<br/>