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| Preface | |
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| Introduction | |
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| Exercises | |
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| Elements of Probability | |
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| Sample Space and Events | |
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| Axioms of Probability | |
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| Conditional Probability and Independence | |
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| Random Variables | |
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| Expectation | |
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| Variance | |
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| Chebyshev's Inequality and the Laws of Large Numbers | |
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| Some Discrete Random Variables | |
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| Continuous Random Variables | |
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| Conditional Expectation and Conditional Variance | |
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| Exercises | |
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| Bibliography | |
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| Random Numbers | |
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| Introduction | |
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| Pseudorandom Number Generation | |
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| Using Random Numbers to Evaluate Integrals | |
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| Exercises | |
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| Bibliography | |
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| Generating Discrete Random Variables | |
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| The Inverse Transform Method | |
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| Generating a Poisson Random Variable | |
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| Generating Binomial Random Variables | |
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| The Acceptance-Rejection Technique | |
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| The Composition Approach | |
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| The Alias Method for Generating Discrete Random Variables | |
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| Generating Random Vectors | |
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| Exercises | |
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| Generating Continuous Random Variables | |
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| Introduction | |
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| The Inverse Transform Algorithm | |
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| The Rejection Method | |
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| The Polar Method for Generating Normal Random Variables | |
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| Generating a Poisson Process | |
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| Generating a Nonhomogeneous Poisson Process | |
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| Simulating a Two-Dimensional Poisson Process | |
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| Exercises | |
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| Bibliography | |
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| The Multivariate Normal Distribution and Copulas | |
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| Introduction | |
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| The Multivariate Normal | |
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| Generating a Multivariate Normal Random Vector | |
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| Copulas | |
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| Generating Variables from Copula Models | |
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| Exercises | |
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| The Discrete Event Simulation Approach | |
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| Introduction | |
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| Simulation via Discrete Events | |
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| A Single-Server Queueing System | |
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| A Queueing System with Two Servers in Series | |
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| A Queueing System with Two Parallel Servers | |
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| An Inventory Model | |
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| An Insurance Risk Model | |
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| A Repair Problem | |
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| Exercising a Stock Option | |
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| Verification of the Simulation Model | |
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| Exercises | |
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| Bibliography | |
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| Statistical Analysis of Simulated Data | |
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| Introduction | |
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| The Sample Mean and Sample Variance | |
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| Interval Estimates of a Population Mean | |
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| The Bootstrapping Technique for Estimating Mean Square Errors | |
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| Exercises | |
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| Bibliography | |
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| Variance Reduction Techniques | |
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| Introduction | |
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| The Use of Antithetic Variables | |
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| The Use of Control Variates | |
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| Variance Reduction by Conditioning | |
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| Stratified Sampling | |
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| Applications of Stratified Sampling | |
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| Importance Sampling | |
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| Using Common Random Numbers | |
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| Evaluating an Exotic Option | |
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| Appendix: Verification of Antithetic Variable Approach When Estimating the Expected Value of Monotone Functions | |
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| Exercises | |
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| Bibliography | |
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| Additional Variance Reduction Techniques | |
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| Introduction | |
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| The Conditional Bernoulli Sampling Method | |
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| Normalized Importance Sampling | |
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| Latin Hypercube Sampling | |
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| Exercises | |
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| Statistical Validation Techniques | |
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| Introduction | |
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| Goodness of Fit Tests | |
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| Goodness of Fit Tests When Some Parameters Are Unspecified | |
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| The Two-Sample Problem | |
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| Validating the Assumption of a Nonhomogeneous Poisson Process | |
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| Exercises | |
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| Bibliography | |
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| Markov Chain Monte Carlo Methods | |
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| Introduction | |
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| Markov Chains | |
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| The Hastings-Metropolis Algorithm | |
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| The Gibbs Sampler | |
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| Continuous time Markov Chains and a Queueing Loss Model | |
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| Simulated Annealing | |
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| The Sampling Importance Resampling Algorithm | |
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| Coupling from the Past | |
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| Exercises | |
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| Bibliography | |
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| Index | |