Simulation and Monte Carlo: With applications in finance and MCMC

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John Wiley & Sons, Apr 4, 2007 - Mathematics - 348 pages
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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.

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 Introduction to simulation and Monte Carlo
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
References
325

9 Solutions
187
Appendix 1 Solutions to problems in Chapter 1
209

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