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.

Manu Steens

Manu works at the Flemish Government in risk management and Business Continuity Management. On this website, he shares his own opinions regarding these and related fields. Since 2012, he has been working at the Crisis Centre of the Flemish Government (CCVO), where he has progressed in BCM, risk management, and crisis management. Since August 2021, he has been a knowledge worker for the CCVO. As of January 2024, he works at the Department of Chancellery and Foreign Affairs of the Flemish Government. Here, he combines BCM, risk management, and crisis management to create a tailored form of resilience management to meet the needs of the Flemish Government.

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