Explorations in Monte Carlo Methods

Undergraduate texts in mathematics.

Authors: Ronald W. Shonkwiler and Franklin Mendivil.

The Monte Carlo method is a technique for analyzing phenomena by means of computer algorithms that use random numbers. This method basically owes its existence to the existence of computers.

In this book the authors give an introduction. It is a book of examples, with every step that is made in theory. In their book, they use the Matlab product to develop program examples, although other programming languages ​​(C, C ++, Pascal, Delphi) can be called just as suitable or more suitable. This approach with program examples makes it very tangible for exact scientists.

Monte Carlo techniques are useful in a wide variety of domains: from estimates of the number Pi, on calculations of mutations in cells, to the running of financial risks when playing in casinos or the evolution of the market.

This book is a very general book for the introduction to Monte Carlo, in the sense that it gives no advantage to a certain type of subject. Although it is a very good book to have a general idea of ​​how Monte Carlo can be used in all kinds of fields, it is not a book that you immediately benefit from as a risk manager. The application of Monte Carlo in the case of machine breakdown, or in financial decisions at a high level is not discussed. This requires more specialized literature.

But as didactic introductory mathematical work to know exactly what Monte Carlo techniques are capable of, it is definitely recommended. If you pass through this book, you are still more layman than specialist, but you are no longer an absolute beginner. You get an idea of ​​the importance of the central limit theorem, and of the Markov chains, and a whole bunch of other things.

For managers who have not enjoyed mathematics for a long time, I have the following advice: try it, your experts might even appreciate it. But if you are lost: no worries, there are still mathematicians out there who are happy to look after your case.