## Simulation and Monte Carlo: With applications in finance and MCMCSimulation 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. 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. 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. |

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### Contents

1 | |

2 Uniform random numbers | 17 |

3 General methods for generating random variates | 37 |

4 Generation of variates from standard distributions | 59 |

5 Variance reduction | 79 |

6 Simulation and finance | 107 |

7 Discrete event simulation | 135 |

8 Markov chain Monte Carlo | 157 |

Appendix 2 Random number generators | 227 |

Appendix 3 Computations of acceptance probabilities | 229 |

Appendix 4 Random variate generators standard distributions | 233 |

Appendix 5 Variance reduction | 239 |

Appendix 6 Simulation and finance | 249 |

Appendix 7 Discrete event simulation | 283 |

Appendix 8 Markov chain Monte Carlo | 299 |

325 | |

### Other editions - View all

Simulation and Monte Carlo: With applications in finance and MCMC J. S. Dagpunar No preview available - 2007 |

### Common terms and phrases

_ end proc acceptance probability algorithm Appendix approximately arrival asset Bayes estimate Bayes estimate failure beta Black–Scholes Brownian motion call option component confidence interval cumulative distribution function denote density proportional Early departure envelope rejection Equation estimate failure rate estimate of price estimated standard error example failure rate pump full conditional gamma geometric Brownian motion Gibbs sampling given hedging importance sampling independently distributed integral interarrival inversion iteration number joint density linear linear congruential Maple procedure marginal density Markov chain MCMC J. S. Dagpunar mean method payoff plot point estimate Poisson process posterior densities prior and posterior probability density function probability of acceptance prospective variate queue random variable realization replications risk-free interest rate seed sequence service duration Show Simulation and Monte skips standard error standard normal Std dev stratification variable stratified sampling Suppose variance reduction ratio volatility Xi+1