Ultimate self-study list

[pj]

> Far and away the best.

Personally I prefer Henrici

[constantine]

I haven't read it, sniffed it, or looked at the cover but you have got to be wrong. I would recommend Needham's book even to people who do not like math.

[constantine]

@Gizmo Look at the head post of [url=/Show%20Post.aspx?PostIDKey=148525]this thread[/url], I gave my extensive self study list with reactions. I think I'm just a little further down the DIY road so maybe my perspective will be useful to you.

[finanzmaster]

As long as you are done with Analysis and Linear Algebra

I would recommend to start from

Pliska - Introduction to Mathematical Finance: Discrete Time Models.

Very readable, directly finance-oriented, written by an originator of risk-neutrality idea.





> 3. "Measure, Integral and Probability" by Marek Capinski , Peter E. Kopp

Good book.



>"Probability with Martingales" by David Williams

Unreadable.



>"Stochastic Differential Equations" by Bernt Øksendal

Maybe the best entry level text book ... since there no others

Instead (or at first) I would recommend

Shreve - Stochastic Calculus for Finance II: Continuous-Time Models

Necessary stuff on SDE is presented very clearly and immediate application to finance follows.



By the self-study there are two principle problems:

1. You cannot clearly distinguish key principles and supplementary details.

2. If you do not understand something there may be no one to ask

[karabouchi!]

No way José!

Øksendal's SDE text is an "entry level text book" if you're a NINJA!



If you want an entry level SDE textbook, I recommend Lawrence Evan's lecture notes, "An Introduction to Stochastic Differential Equations". The notes are available on his website at UC Berkeley department of mathematics, or by direct link, here.

[finanzmaster]

>Øksendal's SDE text is an "entry level text book" if you're a NINJA!

Then I am!

After I got Ito Formula explained (my Prof. followed Shreve) I could readily read Øksendal.

In either case, much more easier that e.g. Protter.



But when a measure-theoretic probability is rigorously introduced in a book I always look whether the author gives and example of an algebra, which is not a sigma-algebra.

Øksendal does not (at least in 5th Edition).

Of course it is not a comprehensive criterion but it usually lets me foresee whether the book is very good or not very



P.S.

Lawrence Evan's lecture notes, which you recommend, are pretty good for beginners

[ddrdouble]

Regarding Oksendal an entry level book, only thing i would add is:



Look at the Existence and Uniqueness proof for SDE's, if you are able to explain every step then you are a true NINJA for me, or the exercise regarding Tanaka formula.



I think, Oksendals book needs much deeper understanding of other math theory like algebra and functional analysis than most people could grasp, but maybe if you are a NINJA,

never met a NINJA, so nevermind

[ruisp666]

Hi guys and gils ,



I joined today and i'm having a great time reading all these posts, and i could not but notice this particular one, since probability theory, and specially the applications by Ito to manifolds, is the perfect blend of measure theory,topology and, why not sometimes, geometry.



How, (I'm not a quant, but just following this thread "flow") about Varadhan's lecture notes on probability theory and stochastic process?It is the perfect companion to david williams very enjoyable book. Of course I don't believe in really self-studying these books or even Olsken's book, but anyway these are my two choices.

By the way, what are you considering by self-stufy?non quantitative background?!

Thank you for your insights,