background for shreve?

[Zeuge]

What kind of mathematical background is required to get the most out of shreve? I have coursework in linear algebra, analysis, multivariate calc, probability and ODE. Do I need measure theory?

 

[Barny]

Measure theory definitely won't hurt, though if you have analysis - you can easily extend what you've learnt to the measure theory you need. So it might be better doing another course which is in a completely new area.

 

[Benjamin H]

Measure theory definitely won't hurt, though if you have analysis - you can easily extend what you've learnt to the measure theory you need. So it might be better doing another course which is in a completely new area.

Agreed. Measure theory is a prerequisite for stochastic calculus and measure-based probability.

 

[wlfgngpck]

Yeah you should definitely have some measure theory before attempting Shreve II. If you've had measure theory, then the first few chapters of Shreve II are routine; if you haven't, they will probably be very difficult.

 

[martingaletrader]

What kind of mathematical background is required to get the most out of shreve? I have coursework in linear algebra, analysis, multivariate calc, probability and ODE. Do I need measure theory?

Shreve II is meant for people like you. You don't need Measure theory to get most out of Shreve. Unless you are reading "Brownian Motion and Stochastic Calculus" which is not aimed at MFE students and is a serious book. I heard there will be an alternative to Shreve II end of this year by some famous prof at another school.

 

[mithrandir]

I did analysis (ugrad) -> Stochastic Processes -> Shreve (independen study) -> Measure Theory.

Lets just say my understanding of Shreve increased much more after Measure Theory.
I found Royden and Fitzpatrick to be excellent.