Simulation

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