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