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

?This book would be immensely useful for any practitioner seeking to learn more about this field, as well as for lecturers seeking a reliable and informative text.? ( <i>Significance</i>, September 2009) <p>"The book does a nice job of discussing, developing, and presenting the mathematical aspects of random processes, random number generation, and Markov chain Monte Carlo (MCMC) methods. I particularly like the notation used and the depth of proofs offered; they are technically correct, well organized, and nicely presented." (<i>Journal of the American Statistical Association</i>, June 2008)</p> <p>?Dagpunar  presents a textbook based on 20-hour courses he has taught for advanced students of mathematics and students of financial mathematics.? (<i>SciTech Book Reviews</i>, June 2007)</p> <p>"?excellent for students and practitioners who don't have previous experience with simulation methods?a great contribution." (<i>MAA Reviews</i>, April 5, 2007)</p>

<p><b>J. S. Dagpunar</b> is the author of <i>Simulation and Monte Carlo: With Applications in Finance and MCMC</i>, published by Wiley.</p>

<a id="Text5" name="Text5"></a>Simulation and Monte Carlo is aimed at students studying for degrees in Mathematics, Statistics, Financial Mathematics, Operational Research, Computer Science, and allied subjects, who wish an up-to-date account of the theory and practice of Simulation. Its distinguishing features are in-depth accounts of the theory of Simulation, including the important topic of variance reduction techniques, together with illustrative applications in Financial Mathematics, Markov chain Monte Carlo, and Discrete Event Simulation. <p>Each chapter contains a good selection of exercises and solutions with an accompanying appendix comprising a Maple worksheet containing simulation procedures. The worksheets can also be downloaded from the web site supporting the book. This encourages readers to adopt a hands-on approach in the effective design of simulation experiments.</p> <p>Arising from a course taught at Edinburgh University over several years, the book will also appeal to practitioners working in the finance industry, statistics and operations research.</p>

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