Elementary Probability Theory

1. Front Matter

   Pages i-xiii

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2. Set

   • Kai Lai Chung, Farid AitSahlia

   Pages 1-19

3. Probability

   • Kai Lai Chung, Farid AitSahlia

   Pages 20-45

4. Counting

   • Kai Lai Chung, Farid AitSahlia

   Pages 46-73

5. Random Variables

   • Kai Lai Chung, Farid AitSahlia

   Pages 74-116

6. Conditioning and Independence

   • Kai Lai Chung, Farid AitSahlia

   Pages 117-163

7. Mean, Variance, and Transforms

   • Kai Lai Chung, Farid AitSahlia

   Pages 164-202

8. Poisson and Normal Distributions

   • Kai Lai Chung, Farid AitSahlia

   Pages 203-253

9. From Random Walks to Markov Chains

   • Kai Lai Chung, Farid AitSahlia

   Pages 254-328

10. Mean-Variance Pricing Model

    • Kai Lai Chung, Farid AitSahlia

    Pages 329-358

11. Option Pricing Theory

    • Kai Lai Chung, Farid AitSahlia

    Pages 359-378

12. Back Matter

    Pages 379-404

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In this edition two new chapters, 9 and 10, on mathematical finance are added. They are written by Dr. Farid AitSahlia, ancien eleve, 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 vocab­ ulary 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 appli­ cability 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.

• Excel
• Markov Chain
• Markov Chains
• Measure
• Multinomial distribution
• Optimization Methods
• Poisson distribution
• Probability distribution
• Probability theory
• Random variable
• STATISTICA
• Stochastic Processes
• operations research
• optimization
• sets
• quantitative finance

"In spite of the original edition of the book being nearly thirty years old, the text still has its role to play in first and second year undergraduate probability courses. It provides an excellent foundation to more advanced courses in the subject."
Short Book Reviews, Vol. 23/3, Dec. 2003

"This edition is the third revision of a text on mathematical probability first published in 1974. The text is aimed at undergraduate mathematics students and is accessible to a general audience. The prose is accurate, entertaining, and dense with historical tidbits. Two concluding chapters on mathematical finance have been added to the eight chapters in the third edition by the second author." The American Statistician, May 2004

From the reviews of the fourth edition:

"The main novelty in the fourth edition of this well-written book is the addition of new chapters … . The new chapters share the friendly yet rigorous style of the former ones. They begin with an account of the financial vocabulary, which is then expounded in probabilistic terms. … Almost thirty years after its first edition, this charming book continues to be an excellent text for teaching and for self study." (Ricardo Maronna, Statistical Papers, Vol. 45 (4), 2004)

• Department of Mathematics, Stanford University, Stanford, USA

  Kai Lai Chung

• DemandTec, Stanford, USA

  Farid AitSahlia