Customer Reviews

Stochastic Processes

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4 star:		(0)
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2 star:		(1)
1 star:		(1)

 

 

I wish I had had this book 20 years ago when I first studied stochastic processes in school: I was very interested in them, but did not have a clue about what they were good for.

The book clarifies why we care about Levy distributions as opposed to plain old normal (Gaussian) distributions. I never understood this before. (If you're too lazy to get the book, I will just say it is because of "fat tails". In the world of finance, many people treat the Law of Large Numbers as if it were the Law of Small Numbers, and don't realize how big the samples have to get sometimes to get the effects you want.)

The book would be suitable for undergraduate math majors or graduate students in physics or finance who have enough mathematical background to follow it. It's over the head of people who can't do calculus and under the chin of graduate math students who probably would prefer something more pure and abstract.

I like this book very much -- It provides an excellent introduction to the subject of stochastic processes from a physical, as opposed to a mahematical/axiomatic, poit of view. It also provides a good introduction to the very basic aspects of mathematical finance. It includes a rather detailed introduction to Levy processes, which is not easily available in introductory textbooks. I highly recommend this book for physics undergrads who wish to learn the subject. Mathematicians may not really find it to their liking.

The idea of writing a book that introduces the reader to stochastic processes from a more modern viewpoint, leading him from physics through to introductory finance is certainly as good as it is natural as it is timely, if not necessary. Clearly, when we physicists contemplate our standard textbooks by Gardiner, Risken, van Kampen, Mazo, etc... in the light of what fine pedagogical works have been produced by modern finance scholars, they stand there as somewhat old-fashioned.

So the idea by the present authors to produce a more modern approach is certainly most welcome and it should be considered as one of the first steps.

Much as I like and adhere to the idea that a brush-up of the context in which stochastic processes is being taught to phyisicists is needed, I truly cannot forgive the authors for
the ill delivery of the material they present. For instance, there are glaring inaccuracies and errors in the rather critical first pages of chapter 2, relating the basic axioms of probability theory following Kolmogorov's approach. If you do that, then do it properly. Similarly, the confused computation on page 37 demonstrating the equivalence of the Fokker-Planck and Langevin equations is unfortunate to have made it into book form.

The chapter on finance is useful, but as ever so often in econophysics literature, somewhat superficial.

I hope that in a forthcoming second edition the authors will take
care to polish the formal background a bit more, maybe push it a bit further, so as to be able to give a clean definition of martingales, for instance. For a neat, if somewhat terse, presentation of much of the material covered here is still think that Stochastic Processes in Polymeric Fluid by H. C. \"Ottinger is still unsurpassed. Alternatively one can turn his/her attention directly to applied financial derivatives textbooks to pick up the essentials or even stick to the old stuff mentioned above.

I read this book 2 years ago and thought it was a great idea to combine the two topics, and it still is. The choice of topics is fantastic and the way it's presented is very good, with lots of useful physical insight. However there are lots of errors in the maths, several steps go unjustified, and just assume the reader to "know what they're talkin' about" or else you're not fit for it. I've read several good books on analysis and probability theory (very good one by Shiryaev using measure theory- I strongly recommend it). Why do these books on analysis go to great lengths in proving their results? That's because you need to justify the approximations that are made. In this book here, most of the approximations are just thrown in into the derivations and you really aren't told what they're good for, and if you're allowed to do that. Typical of physicists to fail to justify their assumptions and just 'leave it to the mathematicians to figure it out' (I'm a physicist BTW, and I hate this lazy attitude). There is a clear lack of rigor.

Having said that, however, I think the authors have done a great job in selecting the topics, and that in a second edition all can be fixed. The book might end up having to be a bit thicker, but who cares, better have a clear monograph without ambiguities rather than some compendium of handwavy explanations as we usually find in the ugly physics literature. Let's face it, physicists are 100 years behind in mathematics, we still don't use the language of modern differential geometry (we use tensor index notation rather than coordinate-free notation), we don't use much analysis and we still don't do stochastic integrals the correct way. Our friends in Economics on the other hand are way ahead of us.