Author | Chung, Kai Lai. author |
---|---|
Title | Elementary Probability Theory [electronic resource] : With Stochastic Processes and an Introduction to Mathematical Finance / by Kai Lai Chung, Farid AitSahlia |
Imprint | New York, NY : Springer New York : Imprint: Springer, 2003 |
Edition | Fourth Edition |
Connect to | http://dx.doi.org/10.1007/978-0-387-21548-8 |
Descript | XIV, 404 p. online resource |
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 Pรณlyaโs 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: Stirlingโs Formula and de Moivre-Laplaceโ 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