18. Itō Calculus

MIT 18.S096 Topics in Mathematics with Applications in Finance, Fall 2013
Instructor: Choongbum Lee

This lecture explains the theory behind Itoíã calculus.

License: Creative Commons BY-NC-SA

[SeikoVanPaath]

Some notable Timestamps:
0:00:25 Itō Calculus
0:12:33 Ito’s lemma
0:40:57 Adapted processes
1:00:18 Change of Measure
1:05:32 Equivalence of probability distributions
1:13:18 Girsanov’s theorem

[chzpan]

Love such type of lecturers who develop everything from the intuitive idea, and derive everything on a blackboard. The only shortcoming of the course was the small size of the blackboard.

[rachelwatsky]

This guy is great! My lecturer in Utrecht is awful, she basically just writes a 2 line proof and somehow we're supposed to figure it all out. Really appreciate that he went through all the steps, especially when he slowed down a bit at 22:55

[jiahuizeng]

he is so great, when explaining these concepts so well, , i cry dont know what i could do without this !

[mariussteicher]

this dude is a legend. Thank you so much Choongbum Lee and MIT.

[rewtnode]

At 24:30 he had exp(mu t + d x) twice in the Taylor expression. But the d x wasn't the differential dx. Instead it should have been exp( mu t + sigma x), which is the same as f(t, x) . It didn't matter though because the next step brought the correct result.

[wonyoutube-mokd]

드디어 이토 적분을 이해했다. 한국인의 자랑 이중범 교수님, 지금은 퀀트 쪽으로 가신 것 같던데.. 나중에 꼭 뵐 수 있는 날이 오기를. 좋은 강의 감사합니다.
Thank you MIT!

[MadeInAsia-qxqk]

this guy is amazing, first time I learned ito formula so clear, thank you bro! Hope I can go study in mit one day!

[krqtkndy]

Typo: Around 30:00, the line below (Q), dS_t should be dS_t/S_t.

[toufikhamdani]

I love this lecture. Really helped grasp the practical use of Ito. Kuddos to prof. Lee and MIT !

[RenormalizedAdvait]

Best discourse on Ito's Lemma, amazing work Prof. Lee.

[استاذعبداللهمحمد]

Peace be upon you, thank you for this valuable lecture

[SlavKinGa]

A minor point. Dr. Lee mentioned a few times "sum of normal variables is normal." This is true for *independent* normal variables but not in general. In the context of the video, the variables were independent (changes of Brownian motions over distinct intervals), so the statements remain correct.

[mrPeredo]

I love this material, thanks MIT. I stared to study Fokker Plank Equation and this is so helpfull.

[liwang]

Omg, you spoke so clearly. Thanks a lot. I will try to send my son to MIT in future.

[Darkpopcatb]

great speaker, explains very good, complex concepts become clear

[TroubleMakery]

That chalk is amazingly soothing and satisfying

[anynamecanbeuse]

23:00 it's exp{ µt + σx }, not exp{ µt + dx }
26:40 it's dSt / St = 1/2 • σ^2dt + σdBt, not dSt = 1/2 • σ^2dt + σdBt
1:06:10 P and P_tilda share the same rank in terms of matrix

[anthonydavolio]

was trying to find a lognormal variance’s dependence on time and a rigorous and long venture was answered in the first minute

[edwardho]

pretty good explanation to the complicated topic