Preface
Overview
New to This Edition
Chapter Descriptions
Thanks
Chapter 1. Introduction
Exercises
Chapter 2. Elements of Probability
2.1 Sample Space and Events
2.2 Axioms of Probability
2.3 Conditional Probability and Independence
2.4 Random Variables
2.5 Expectation
2.6 Variance
2.7 Chebyshev’s Inequality and the Laws of Large Numbers
2.8 Some Discrete Random Variables
2.9 Continuous Random Variables
2.10 Conditional Expectation and Conditional Variance
Exercises
References
Chapter 3. Random Numbers
Introduction
3.1 Pseudorandom Number Generation
3.2 Using Random Numbers to Evaluate Integrals
Exercises
References
Chapter 4. Generating Discrete Random Variables
4.1 The Inverse Transform Method
4.2 Generating a Poisson Random Variable
4.3 Generating Binomial Random Variables
4.4 The Acceptance– Rejection Technique
4.5 The Composition Approach
4.6 The Alias Method for Generating Discrete Random Variables
4.7 Generating Random Vectors
Exercises
Chapter 5. Generating Continuous Random Variables
Introduction
5.1 The Inverse Transform Algorithm
5.2 The Rejection Method
5.3 The Polar Method for Generating Normal Random Variables
5.4 Generating a Poisson Process
5.5 Generating a Nonhomogeneous Poisson Process
5.6 Simulating a Two-Dimensional Poisson Process
Exercises
References
Chapter 6. The Multivariate Normal Distribution and Copulas
Introduction
6.1 The Multivariate Normal
6.2 Generating a Multivariate Normal Random Vector
6.3 Copulas
6.4 Generating Variables from Copula Models
Exercises
Chapter 7. The Discrete Event Simulation Approach
Introduction
7.1 Simulation via Discrete Events
7.2 A Single-Server Queueing System
7.3 A Queueing System with Two Servers in Series
7.4 A Queueing System with Two Parallel Servers
7.5 An Inventory Model
7.6 An Insurance Risk Model
7.7 A Repair Problem
7.8 Exercising a Stock Option
7.9 Verification of the Simulation Model
Exercises
References
Chapter 8. Statistical Analysis of Simulated Data
Introduction
8.1 The Sample Mean and Sample Variance
8.2 Interval Estimates of a Population Mean
8.3 The Bootstrapping Technique for Estimating Mean Square Errors
Exercises
References
Chapter 9. Variance Reduction Techniques
Introduction
9.1 The Use of Antithetic Variables
9.2 The Use of Control Variates
9.3 Variance Reduction by Conditioning
9.4 Stratified Sampling
9.5 Applications of Stratified Sampling
9.6 Importance Sampling
9.7 Using Common Random Numbers
9.8 Evaluating an Exotic Option
9.9 Appendix: Verification of Antithetic Variable Approach When Estimating the Expected Value of Monotone Functions
Exercises
References
Chapter 10. Additional Variance Reduction Techniques
Introduction
2 The Conditional Bernoulli Sampling Method
3 Normalized Importance Sampling
4 Latin Hypercube Sampling
Exercises
Chapter 11. Statistical Validation Techniques
Introduction
11.1 Goodness of Fit Tests
11.2 Goodness of Fit Tests When Some Parameters Are Unspecified
11.3 The Two-Sample Problem
11.4 Validating the Assumption of a Nonhomogeneous Poisson Process
Exercises
References
Chapter 12. Markov Chain Monte Carlo Methods
Introduction
12.1 Markov Chains
12.2 The Hastings–Metropolis Algorithm
12.3 The Gibbs Sampler
12.4 Continuous time Markov Chains and a QueueingLoss Model
12.5 Simulated Annealing
12.6 The Sampling Importance Resampling Algorithm
12.7 Coupling from the Past
Exercises
References
Index
