Preface. Glossary.
1 Introduction to simulation and Monte Carlo.
1.1 Evaluating a definite integral.
1.2 Monte Carlo is integral estimation.
1.3 An example.
1.4 A simulation using Maple.
1.5 Problems.
2 Uniform random numbers.
2.1 Linear congruential generators.
2.2 Theoretical tests for random numbers.
2.3 Shuffled generator.
2.4 Empirical tests.
2.5 Combinations of generators.
2.6 The seed(s) in a random number generator.
2.7 Problems.
3 General methods for generating random variates.
3.1 Inversion of the cumulative distribution function.
3.2 Envelope rejection.
3.3 Ratio of uniforms method.
3.4 Adaptive rejection sampling.
3.5 Problems.
4 Generation of variates from standard distributions.
4.1 Standard normal distribution.
4.2 Lognormal distribution.
4.3 Bivariate normal density.
4.4 Gamma distribution.
4.5 Beta distribution.
4.6 Chi-squared distribution.
4.7 Student's t distribution.
4.8 Generalized inverse Gaussian distribution.
4.9 Poisson distribution.
4.10 Binomial distribution.
4.11 Negative binomial distribution.
4.12 Problems.
5 Variance reduction.
5.1 Antithetic variates.
5.2 Importance sampling.
5.3 Stratified sampling.
5.4 Control variates.
5.5 Conditional Monte Carlo.
5.6 Problems.
6 Simulation and finance.
6.1 Brownian motion.
6.2 Asset price movements.
6.3 Pricing simple derivatives and options.
6.4 Asian options.
6.5 Basket options.
6.6 Stochastic volatility.
6.7 Problems.
7 Discrete event simulation.
7.1 Poisson process.
7.2 Time-dependent Poisson process.
7.3 Poisson processes in the plane.
7.4 Markov chains.
7.5 Regenerative analysis.
7.6 Simulating a G/G/1 queueing system using the three-phase method.
7.7 Simulating a hospital ward.
7.8 Problems.
8 Markov chain Monte Carlo.
8.1 Bayesian statistics.
8.2 Markov chains and the Metropolis-Hastings (MH) algorithm.
8.3 Reliability inference using an independence sampler.
8.4 Single component Metropolis-Hastings and Gibbs sampling.
8.5 Other aspects of Gibbs sampling.
8.6 Problems.
9 Solutions.
9.1 Solutions 1.
9.2 Solutions 2.
9.3 Solutions 3.
9.4 Solutions 4.
9.5 Solutions 5.
9.6 Solutions 6.
9.7 Solutions 7.
9.8 Solutions 8.
Appendix 1: Solutions to problems in Chapter 1.
Appendix 2: Random Number Generators.
Appendix 3: Computations of acceptance probabilities.
Appendix 4: Random variate generators (standard distributions).
Appendix 5: Variance Reduction.
Appendix 6: Simulation and Finance.
Appendix 7: Discrete event simulation.
Appendix 8: Markov chain Monte Carlo.
References.
Index.
