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

Elementary Probability Theory: With Stochastic Processes and an Introduction to Mathematical Finance
Catalogue Information
Field name Details
Dewey Class 519.2
Title Elementary Probability Theory ([EBook]) : With Stochastic Processes and an Introduction to Mathematical Finance / by Kai Lai Chung, Farid AitSahlia.
Author Chung, Kai Lai , 1917-2009
Added Personal Name AitSahlia, Farid
Other name(s) SpringerLink (Online service)
Edition statement Fourth Edition.
Publication New York, NY : Springer , 2003.
Physical Details XIV, 404 pages : online resource.
Series Undergraduate texts in mathematics 0172-6056
ISBN 9780387215488
Summary Note 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.:
Contents note 1 Set -- 1.1 Sample sets -- 1.2 Operations with sets -- 1.3 Various relations -- 1.4 Indicator -- Exercises -- 2 Probability -- 2.1 Examples of probability -- 2.2 Definition and illustrations -- 2.3 Deductions from the axioms -- 2.4 Independent events -- 2.5 Arithmetical density -- Exercises -- 3 Counting -- 3.1 Fundamental rule -- 3.2 Diverse ways of sampling -- 3.3 Allocation models; binomial coefficients -- 3.4 How to solve it -- Exercises -- 4 Random Variables -- 4.1 What is a random variable? -- 4.2 How do random variables come about? -- 4.3 Distribution and expectation -- 4.4 Integer-valued random variables -- 4.5 Random variables with densities -- 4.6 General case -- Exercises -- Appendix 1: Borel Fields and General Random Variables -- 5 Conditioning and Independence -- 5.1 Examples of conditioning -- 5.2 Basic formulas -- 5.3 Sequential sampling -- 5.4 Pólya’s urn scheme -- 5.5 Independence and relevance -- 5.6 Genetical models -- Exercises -- 6 Mean, Variance, and Transforms -- 6.1 Basic properties of expectation -- 6.2 The density case -- 6.3 Multiplication theorem; variance and covariance -- 6.4 Multinomial distribution -- 6.5 Generating function and the like -- Exercises -- 7 Poisson and Normal Distributions -- 7.1 Models for Poisson distribution -- 7.2 Poisson process -- 7.3 From binomial to normal -- 7.4 Normal distribution -- 7.5 Central limit theorem -- 7.6 Law of large numbers -- Exercises -- Appendix 2: Stirling’s Formula and de Moivre-Laplace’ Theorem -- 8 From Random Walks to Markov Chains -- 8.1 Problems of the wanderer or gambler -- 8.2 Limiting schemes -- 8.3 Transition probabilities -- 8.4 Basic structure of Markov chains -- 8.5 Further developments -- 8.6 Steady state -- 8.7 Winding up (or down?) -- Exercises -- Appendix 3: Martingale -- 9 Mean-Variance Pricing Model -- 9.1 An investments primer -- 9.2 Asset return and risk -- 9.3 Portfolio allocation -- 9.4 Diversification -- 9.5 Mean-variance optimization -- 9.6 Asset return distributions -- 9.7 Stable probability distributions -- Exercises -- Appendix 4: Pareto and Stable Laws -- 10 Option Pricing Theory -- 10.1 Options basics -- 10.2 Arbitrage-free pricing: 1-period model -- 10.3 Arbitrage-free pricing: N-period model -- 10.4 Fundamental asset pricing theorems -- Exercises -- General References -- Answers to Problems -- Values of the Standard Normal Distribution Function.
System details note Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site http://dx.doi.org/10.1007/978-0-387-21548-8
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