Ebook: Elementary Probability Theory: With Stochastic Processes and an Introduction to Mathematical Finance

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.

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This book is an introductory textbook on probability theory and its applications. Basic concepts such as probability measure, random variable, distribution, and expectation are fully treated without technical complications. Both the discrete and continuous cases are covered, but only the elements of calculus are used in the latter case.

The emphasis is on essential probabilistic reasoning, amply motivated, explained and illustrated with a large number of carefully selected samples. Special topics include: combinatorial problems, urn schemes, Poisson processes, random walks, and Markov chains. Problems and solutions are provided at the end of each chapter. Its elementary nature and conciseness make this a useful text not only for mathematics majors, but also for students in engineering and the physical, biological, and social sciences.

This edition adds two chapters covering introductory material on mathematical finance as well as expansions on stable laws and martingales. Foundational elements of modern portfolio and option pricing theories are presented in a detailed and rigorous manner. This approach distinguishes this text from others, which are either too advanced mathematically or cover significantly more finance topics at the expense of mathematical rigor.

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This book is an introductory textbook on probability theory and its applications. Basic concepts such as probability measure, random variable, distribution, and expectation are fully treated without technical complications. Both the discrete and continuous cases are covered, but only the elements of calculus are used in the latter case.

The emphasis is on essential probabilistic reasoning, amply motivated, explained and illustrated with a large number of carefully selected samples. Special topics include: combinatorial problems, urn schemes, Poisson processes, random walks, and Markov chains. Problems and solutions are provided at the end of each chapter. Its elementary nature and conciseness make this a useful text not only for mathematics majors, but also for students in engineering and the physical, biological, and social sciences.

This edition adds two chapters covering introductory material on mathematical finance as well as expansions on stable laws and martingales. Foundational elements of modern portfolio and option pricing theories are presented in a detailed and rigorous manner. This approach distinguishes this text from others, which are either too advanced mathematically or cover significantly more finance topics at the expense of mathematical rigor.

Content:
Front Matter....Pages i-xiii
Set....Pages 1-19
Probability....Pages 20-45
Counting....Pages 46-73
Random Variables....Pages 74-116
Conditioning and Independence....Pages 117-163
Mean, Variance, and Transforms....Pages 164-202
Poisson and Normal Distributions....Pages 203-253
From Random Walks to Markov Chains....Pages 254-328
Mean-Variance Pricing Model....Pages 329-358
Option Pricing Theory....Pages 359-378
Back Matter....Pages 379-404

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This book is an introductory textbook on probability theory and its applications. Basic concepts such as probability measure, random variable, distribution, and expectation are fully treated without technical complications. Both the discrete and continuous cases are covered, but only the elements of calculus are used in the latter case.

The emphasis is on essential probabilistic reasoning, amply motivated, explained and illustrated with a large number of carefully selected samples. Special topics include: combinatorial problems, urn schemes, Poisson processes, random walks, and Markov chains. Problems and solutions are provided at the end of each chapter. Its elementary nature and conciseness make this a useful text not only for mathematics majors, but also for students in engineering and the physical, biological, and social sciences.

This edition adds two chapters covering introductory material on mathematical finance as well as expansions on stable laws and martingales. Foundational elements of modern portfolio and option pricing theories are presented in a detailed and rigorous manner. This approach distinguishes this text from others, which are either too advanced mathematically or cover significantly more finance topics at the expense of mathematical rigor.

Content:
Front Matter....Pages i-xiii
Set....Pages 1-19
Probability....Pages 20-45
Counting....Pages 46-73
Random Variables....Pages 74-116
Conditioning and Independence....Pages 117-163
Mean, Variance, and Transforms....Pages 164-202
Poisson and Normal Distributions....Pages 203-253
From Random Walks to Markov Chains....Pages 254-328
Mean-Variance Pricing Model....Pages 329-358
Option Pricing Theory....Pages 359-378
Back Matter....Pages 379-404
....