Simulation and Monte Carlo With applications in finance and MCMC [Paperback]

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.

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 oflãƒ