Stochastic Calculus Help

[Jasper S]

Hello everyone!

I just started my Masters in mathematics with specialization towards financial mathematics a couple of weeks ago. One of the first courses is Stochastic Calculus and I am having a hard time with it, all the way from notations to calculations. Everything feels abstract and I have to google every term to be able to get somewhere... I could really use some suggestions regarding how to study it and what kind of material that is useful.

My background is:
BSc. Industrial Engineering and BSc. Economics
Math courses: Linear Algebra, Calculus and Multivariable Calculus, Differential EQ, Fourier Analysis, Mathematical Statistics.

The book we are using is: "Fima C Klebaner - Introduction to Stochastic Calculus with Applications" http://www.amazon.com/Introduction-Stochastic-Calculus-Applications-Klebaner/dp/186094566X

So my question is there any other book I could look in to, video lectures or some other useful materials that could help me on the way?

Thank you in advance,
JS

 

[throll]

check out the video lecture here http://www.utstat.utoronto.ca/sjaimung/courses/mmf1928/content2010.htm maybe it will help, good luck
ps: i haven't seen the video lectures

 

[Daniel Duffy]

At one level all these stochastic courses put the cart before the horse. The pedagogica error is not doing a decent course first in measure theory and Lebesgue integral (speaking as erstswhile 2nd year maths student).

Many people are having/had difficulty. I fear your background in Maths may not be rigorous enough. It's like goinng from orange belt to brown belt by skipping green and blue. It is so bad.

Now that you ask, I have audio/videos lectures on this and related issues


http://www.datasimfinancial.com/course_detail.php?courseId=18

send me an email if you wish to chat.

 

[Daniel Duffy]

I recommend "Brownian Motion Calculus" by Ubbo Wiersema (Wiley)

 

[Jasper S]

Thank you both for the quick replies! I think I will get the book by Ubbo Wiersema for starters and see how it goes, and also study the basics of Lebesgue and Measure Theory.

If theres anyone else out there who had the same issues with Stochastic Calculus please feel free to share your opinions

JS

 

[Daniel Duffy]

The Schaum "Real Variable" by Spiegel is a no-nonsense.

Stay away from Rudin.

 

[Daniel Duffy]

check out the video lecture here http://www.utstat.utoronto.ca/sjaimung/courses/mmf1928/content2010.htm maybe it will help, good luck
ps: i haven't seen the video lectures

What do people think of hand-written formulae?

 

[Jasper S]

Thank you for your input Daniel Duffy! What are your thoughts on "Fima C Klebaner - Introduction to Stochastic Calculus with applications"?

 

[Daniel Duffy]

Thank you for your input Daniel Duffy! What are your thoughts on "Fima C Klebaner - Introduction to Stochastic Calculus with applications"?

Unfortunately, I don't know this book.


This one might be worth looking at

http://www.amazon.com/Elementary-Stochastic-Calculus-Statistical-Probability/dp/9810235437

 

[bordingj]

http://web.media.mit.edu/~lifton/snippets/measure_theory.pdf

 

[Johan KJ]

Are you from Denmark Jasper? If yes, then I would buy Ernst Hansen - Measure Theory.

 

[Alexandre Chretien]

Introduction to Probability Models by Sheldon M Ross.

 

[Earl Chua]

The Schaum "Real Variable" by Spiegel is a no-nonsense.

Stay away from Rudin.

What's wrong with Rudin?

 

[Daniel Duffy]

What's wrong with Rudin?

Nothing wrong whatsover; I used it in my first year undergrad maths. I have seen that not all maths students found it easy and my hunch is that it _could_ scare off some people. Hence the Plan B Schaum.

Rudin assumes a certain level of mathematiclly maturity (e.g. Dedekind cuts).

 

[Jay YK Kim]

http://www.amazon.com/Stochastic-Calculus-Finance-Binomial-Textbooks/dp/0387249680/ref=sr_1_2?ie=UTF8&qid=1381950245&sr=8-2&keywords=stochastic calculus

I'm using volume 1 and volume 2 of this book and I believe that the contents are very intuitive. I like them so far, although it's still not easy to follow.