Stochastic Differential Equations

[Menime]

Hi,

I've been reading theoretical implications of stochastic differential equations. I want to know what pre-requisites are required before i foray into proper study of this topic.I'm fairly comfortable with partial differentials and probability theory. But, the use of sigma- algebra baffles me. Can someone please mention the background knowledge one needs to have before starting with stochastic differentials.?
Also, can someone please suggest reading materials for the same?

 

[CasanovaJ]

As far as your reference to sigma algebras go, I'm about two months into an MFE program, the stochal course is pretty heavy on measure theory, and I've actually been pretty curious as to whether it's actually necessary, or if it's just a situation of the professor being more theoretical with it than he has to be... wouldn't mind if someone knowledgeable weighs in on this one

 

[Daniel Duffy]

Why so much measure theory?????

http://www.wilmott.com/messageview.cfm?catid=8&threadid=95199&FTVAR_MSGDBTABLE=

 

[yetanotherquant]

Hi Menime,
All you need is a proper introduction to the measure theory. Have a look at mine: http://www.yetanotherquant.de/#MeasureTheoryBook

 

[Jedison]

I personally don't think the measure theory stuff is all that important. It's good to know, you'll need to understand what filtration is but outside of that I don't think you really use it a ton. It's important to understand taylor expansions and some basics from a pde course.

 

[Menime]

Thanks a lot, people. I reckon a basic understanding of measure theory is required at least to begin with.
This gives me a direction to start and structure my study.

 

[yetanotherquant]

I personally don't think the measure theory stuff is all that important. It's good to know, you'll need to understand what filtration is but outside of that I don't think you really use it a ton. It's important to understand taylor expansions and some basics from a pde course.

Well, if you really wan't to understand what the risk-neutral pricing is (and not just to learn it in a dogmatic way), you need to understand measure theory and in particular the change of measure.
Ok, Black-Scholes can be done without measure ... but Black-76 cannot (at least in a consistent way)
And in LIBOR Market Model the measure theoretic insights (T-Forward measures) are really great.
Have a look at my tutorial: http://www.yetanotherquant.de/libor/tutorial.pdf