Help on finding a suitable book: stochastic calculus

[ChrisDerick]

Hey all,

would need help finding a suitable book for my stochastic calculus readings. I have physics background, but I have not touched stochastic calculus at all. I have basic working knowledge in probability, PDE, vector calculus.

There are some suggestions to start out with Shreve's Stochastic Calculus for finance II. However first few pages are pretty intimidating - fancy ways to define cumulative distribution function, etc etc.

any suggestion of alternative books will be much appreciated. Thanks!

 

[Polter]

Eventually, IMHO you should be able to get over it (read: don't let yourself be intimidated!) and go through Shreve: it's actually a relatively straightforward / introductory book -- mostly using Wiener Processes / no general Lévy Processes framework (let alone semimartingales) / no general theory of stochastic processes (no optional filtrations / previsible filtrations / progressive measurability, etc.). It hardly uses measure theory (although it does occasionally, when it really matters--say, in the context of the Girsanov theorem). In other words: a pretty good intro book!

If you'd like a pre-intro book Baxter & Rennie is actually pretty good ("Financial Calculus: An Introduction to Derivative Pricing").

 

[Daniel Duffy]

Hey all,


[...] stochastic calculus for finance. However first few pages are pretty intimidating - fancy ways to define cumulative distribution function, etc etc.

I agree.

Trying to condense measure theory, Lebesque, random variable and probability theory in chapter 1 means that you will not understand much of the other 10 chapters.

In all fairness, this seems to be the accepted/standard approach. It's a shame and academically irresponsible IMO.

Undergrad maths degrees need a full 3 terms (2nd year) to do these any justice.


Get the Schaum book on Probability, Random Variables and Random Processes and take it from there.

 

[ChrisDerick]

I agree.

Trying to condense measure theory, Lebesque, random variable and probability theory in chapter 1 means that you will not understand much of the other 10 chapters.

In all fairness, this seems to be the accepted/standard approach. It's a shame and academically irresponsible IMO.

Undergrad maths degrees need a full 3 terms (2nd year) to do these any justice.


Get the Schaum book on Probability, Random Variables and Random Processes and take it from there.

Thanks Daniel & Polter. I'll take a look on suggested books.
Anyway, I've noticed the second chapter isn't that bad, as long as you can go through the definition fine. Thanks all.