Which book is best for my self-study of stochastic calculus?

bootstrap

bootstrap

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Hi everybody,

I have a master's in statistics. It has been almost a decade but my knowledge of probability had (once) gone as far as the following concepts : the probability triple, the monotone and dominated convergence theorems, martingales, and very vaguely the radon-nikodym derivative (you get the idea). Probably need a few weeks of quiet study to review all these and get back up to speed.

Anyway, I am now aiming to make a career switch from being a buy-side macro economist to a buy-side quant, and I think learning about stochastic calculus would be helpful (avoided that course back in the day because the professor was a known disaster). My aim is NOT to become so acquainted with the subject so I could begin dong Phd research on the topic. Just want to be solidly grounded enough to be an effective and efficient quant.

Need a book for self-study and I have narrowed down my list to the these two. Which one would you think is better for me? Or would there be a 3rd better option I am not aware of? My goal is to get as much out of a book as quickly as possible, to the point that I am totally comfortable with the key concepts, how they have come about, and how they are applied in finance. Your advice is much appreciated, thank you so much!

1. Shreve: Stochastic Calculus and Finance
2. Michael Steele: Stochastic Calculus and Financial Applications
 
CrossGamma said:
So..? OP is asking about a book for stochastic calculus
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Depends how you define stochastic calculus.
Because you will only half understand stochastic calculus by studying theoretical SDEs. It is too one-sided; besides most SDEs don't have analytic solutions.

Ideally, you need to learn Measure Theory and Lebesgue Integration as foundation. How in earth will you understand Girsanov and Radon-Nikodym otherwise?
 
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Daniel Duffy said:
Depends how you define stochastic calculus.
Because you will only half understand stochastic calculus by studying theoretical SDEs. It is too one-sided; besides most SDEs don't have analytic solutions.

Ideally, you need to learn Measure Theory and Lebesgue Integration as foundation. How in earth will you understand Girsanov and Radon-Nikodym otherwise?
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This is what makes Shreve's volume 2 great, he packages the necessary measure theoretic results into the first two chapters so that one is able to understand results such as the ones you mention. Of course, his treatment is surface level, but nonetheless it is sufficient to understand the motivation behind results like that of Girsanov.

Learning stochastic calculus does not require you to learn numerical methods for SDEs. The main ingredients, e.g. brownian motion and martingales, stochastic integration, Itos lemma, Girsanov and Feynman-Kac, SDEs, in my opinion have nothing to do with numerical methods at the surface. Where numerical methods make sense is in a second course -- a first course in stochastic calculus should focus on the (pure) mathematics, and this is exactly what Shreve volume 2 does.
 
Qui-Gon said:
This is what makes Shreve's volume 2 great, he packages the necessary measure theoretic results into the first two chapters so that one is able to understand results such as the ones you mention. Of course, his treatment is surface level, but nonetheless it is sufficient to understand the motivation behind results like that of Girsanov.

Learning stochastic calculus does not require you to learn numerical methods for SDEs. The main ingredients, e.g. brownian motion and martingales, stochastic integration, Itos lemma, Girsanov and Feynman-Kac, SDEs, in my opinion have nothing to do with numerical methods at the surface. Where numerical methods make sense is in a second course -- a first course in stochastic calculus should focus on the (pure) mathematics, and this is exactly what Shreve volume 2 does.
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That's why I prefer Glasserman .. he integrates the two approaches.
Horses for courses.
 
Quasar Chunawala said:
@bootstrap - I am self-learning and working through the exercises of (1). I'd be glad to speak/connect with you sometime.
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I think if you want to study stochastic calculus deeply, Hui Hsuing Kuo's Introduction to Stochastic Integration might be a good mathematical spin to the topic. I am going through this book myself, along with David William's Probability with Martingales. Thomas Mikosch's Introduction to Stochastic Calculus might also be a good entry point, if talking through a mathematical stand point.
 
My two cents: I think Bjork's "Arbitrage Theory in Continuous Time" is an underrated gem — balances intuition, formal rigor, and applications really well.
 
Daniel Duffy said:
Again, get Glasserman >> all others


and Kloeden/Platen



Study and program them and then proclaim victory.
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I liked the book : A first course in StoCal, by LP Arguin, and have a copy of it on my desk.

It doesn't do handwaving. The proofs are first motivated, and some are left as exercises. There are also numerical projects. Accessible to an undergrad (with just some knowledge of algebra/calculus).

Also, for concepts, I found the book by Bjork to be invaluable.
 

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