17. Stochastic Processes II

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

This lecture covers stochastic processes, including continuous-time stochastic processes and standard Brownian motion.

License: Creative Commons BY-NC-SA

[RamoSFTT]

University professors, watch and learn. This is how it should be taught!! Spent a week going through my lecture notes and several book and all it took is this video to make it all stick. Thank you Choongbum Lee and thank you MIT.

[meme_eternity]

00:00 Stochastic processes and continuous time

08:48 Brownian motion is a continuous probability distribution

16:49 Brownian motion is the limit of simple random walks.

24:26 Brownian motion is a key model used in financial markets and other fields.

31:45 The probability that the maximum stock price is greater than a at time t is equal to 2 times the probability that the Brownian motion is greater than a.

41:21 Brownian motion has certain properties

51:11 Brownian motion has quadratic variation equal to zero

59:12 Brownian motion and Ito's calculus are used to model stock prices and estimate infinitesimal differences.

1:07:30 Ito's lemma is a highly nontrivial result that allows for calculus with Brownian motion.

1:15:38 Calculus using Brownian motion is complicated

[nadekang]

Great lecture. When I was in Japan, one of my Japanese professors is also called Ito, and later in his fin. derivatives class, I learned that Ito's Lemma's Kiyoshi Ito was his grandpa.

[fastundercoverkitgoogle]

Choongbum is a legend. The things he is making crystal clear to understand in 1 hour would take you days going over the textbooks and studying the derivations

[SeikoVanPaath]

Some notable Timestamps:
0:00:24 Recap (Lecture 5)
0:02:14 Continuous-time stochastic process
0:06:12 (Standard) Brownian Motion
0:48:08 Quadratic variation theorem

[nmecht]

It's really great when you can see that somebody who clearly knows what they are talking about still takes care to present his knowledge with humility and openness. Great lecturers know enough about their subjects to realize how much they don't know.

[mhkhusyairi]

Clearly the best lecturer in this course

[Anonymous-lwzy]

Wow! What a delightfully clear explanation of Ito's lemma! I love the way Lee steps through his explanations - at each point showing the equation, then illustrating it geometrically, then discussing it in plain English, and then discussing its broader significance. He gives three different ways to understand each step, then ties it all together into the broader mathematical context. Lee is an amazingly gifted teacher!

[wayneqwele]

What a profoundly simple explanation of that dB^2=dt result.

[andreapaps]

"It looks right but Its wrong for reasons you dont know yet" - Choongbum Lee

Gonna drop this in my next argument :D

[hongkyukim]

Dr. Lee is amazing. This is literally the best explanation I've had about Ito's Lemma.

[zonghaoyang]

I really like Choonbum's teaching style of how he can break the topic and describe the incentives of each theory. And it is really easier for me to follow as well when professors can write them down on blackboards. I agree now that one can teach math only on blackboard.

[NgardSC]

I hope MIT will upload more lessons from Dr Lee. Very pleasant to listen, you can tell he's a humble and knowledgeable person.

[er]

Really enjoyed the lecture. I Made like a bandit sitting on my bed in Jakarta attending this beautiful class in mit Boston many years ago. Thanks ocw and prof choongbum lee

[mtyjy]

its even much more useful to study with these few videos about stochastic process than to actually attend lecture at a current university

[maxwellsdaemon]

The more I watch this series of videos on Stochastic processes, the more I realize that while they are good and give some interesting results, the sloppiness of the presentation also shows more and more. Another example is the argument made in 58:35. I thought the presenter should have made a comment about the standard deviation of the Y_i, not just the expectation of the Y_i

[econmajor]

Thanks so much, Choongbum.

Beautiful lecture that delivers important contents, which could have been confusing, in a concise manner. Appreciate your lecture.

[richardk]

This was a great lecture on Brownian motion! Choongbum is truly really talented as a lecturer. It's too bad that he's no longer in academia.

[muntazirabidi]

By far one of the most clearest lectures on this topic! thank you for uploading.

[yongliangyang]

A good lecture that clearly explains the motivation. Even good for engineering people.