Itô Calculus(en.wikipedia.org)
en.wikipedia.org
Itô Calculus
https://en.wikipedia.org/wiki/It%C3%B4_calculus
2 comments
Walter Rudin's real analysis slaughtered me in school. I can't imagine getting to measure spaces and Lebesgue integrals. Respect to people who get this.
The only person I know who has a firm grasp of this, earns about $20 million a year at a hedge fund.
First of all you don't need a firm grasp of ito integration to make money at a hedge fund, not even 20MM. Conversely it's not like they just give you 20MM once you've passed your quals.
Second of all it's really not that hard. There are a ton of undergrad books that cover it (along with the necessary measure theory). And then even the bible (oksendahl) can be pushed through with a lot of patience.
At the end of the day ito's integral is defined like a whole bunch of other exotic integrals (as a limit of sums of simple functions, and extended with DCT cf. existence in the wiki) - once you've seen one such derivation you've seen em all. And btw there are plenty of other integrals against processs - like the stratonovich integral (which okay is just a shifted ito integral).
You have to understand that defining things is literally all mathematicians do. once in a while they get lucky and it's useful but the act of defining itself is not some stroke of brilliance.
Second of all it's really not that hard. There are a ton of undergrad books that cover it (along with the necessary measure theory). And then even the bible (oksendahl) can be pushed through with a lot of patience.
At the end of the day ito's integral is defined like a whole bunch of other exotic integrals (as a limit of sums of simple functions, and extended with DCT cf. existence in the wiki) - once you've seen one such derivation you've seen em all. And btw there are plenty of other integrals against processs - like the stratonovich integral (which okay is just a shifted ito integral).
You have to understand that defining things is literally all mathematicians do. once in a while they get lucky and it's useful but the act of defining itself is not some stroke of brilliance.