Stochastic Calculus and Processes: Introduction (Markov, Gaussian, Stationary, Wiener, and Poisson)

[@rajanalexander4949]

Once you get past the uncanny valley voice . . . the content and explanation is really excellent; thank you!

[@lipaka123]

Fantastic, crisp and to the point! Thanks a lot.

[@quantpie]

@Viswanadha Reddy, thank you!

[@Deshammanideep]

Hello sir, Are you preparing for exam ?

[@gerardsho500]

well done, best tutorial on stochastic by miles

[@quantpie]

Thanks Gerard!

[@cristinastoica2630]

I agree with Gerard: this video is short and sweet, at the point.

[@quantpie]

Thanks Cristina!

[@camillesylvain9202]

Hi, can you give us the code you use to create your graphic?

[@quantpie]

many thanks for the comment! What particular graphic please?

[@abhinavsaxena2388]

I am new to computational finance. Guess this should be the first lecture. But , from the videos available , what should be the next 5 topics in order to further develop understanding on stochastic processes ?

[@quantpie]

The best would be to start with the Black Scholes's series. If you encounter a topic that does not make sense then please look it up in the Stochastic calculus playlist. The simplified Stochastic and quant finance series also would be a good place to start if you don't want to jump straight into the Black scholes. Good luck, and keep it up! many thanks!

[@NathanCrock]

When I see stochastic processes plotted, there always seems to be an implicit summation taking place. For example, the indexed random variable you defined Z_i takes only two values, +1 or -1. Yet when you plot Z_i vs the indices, for example at 3:03, Z_2 somehow takes the value of 2, which is not possible given its definition. So the y-axis is not really Z_i. I find this implicit summing also the case with Brownian motion, each B_i is a distribution over displacements, yet the process at i is the sum of all displacements up to i. My question is, why is this implicit summing not explicit? Also, if there is implicit summing, why not simply define the stochastic process to be the sum?? S_i = sum_i Z_i, then the plot would be consistent with the idea that a stochastic process is an indexed collection of random variables.

[@quantpie]

hello! Great question as always! In most cases, we indeed see the stochastic process as sum of increments, so great observation; however, the definition of a stochastic process is ‘loose’, and this is on purpose because leaving it loosely defined helps view the process from various perspectives - e.g., it can be viewed as a collection of random variables, in terms of joint distribution of the process values in certain cases, and as ensemble of paths (e.g., fixed time interval say and what view the process as a random function). Index is usually time, but it can be other things. Index can also be a random variable - say gamma (we are going to cover this aspect at some point.) So the general definition covers a lot of different perspectives. In this particular case, what we are plotting is not Z_i, but the net position of a player who is playing a game on the outcome of a sequence of Z_i’s, so the stochastic process is the net position, sum of individual outcomes. Hope this helps!

[@NathanCrock]

@@quantpie it helps a great deal! It is nice to know that my notion of a stochastic process is narrow. For now, I have few examples and a limited understanding. That is why your lectures are so helpful. Looking forward to more examples and seeing the bigger picture! Thanks again

[@quantpie]

hope all is well! When you get a chance, please do check out the latest video - generalisation of Poisson. It gives some examples of processes with indices other than time: location of trees in a forest, stars in the universe.

[@NathanCrock]

@@quantpie You can count on it! Thank you for your efforts.

[@iliTheFallen]

First off thank you for the great classes. How am I supposed to cite you in a paper? Would you mind providing me with a bibtex stuff?

[@quantpie]

Hello again! And you can generate the reference using this website: www.mybib.com/tools/harvard-referencing-generator Actually it searches the web as well to find the video!

[@miquelnogueralonso2576]

Can we have the slides ?

[@quantpie]

Hello, and many thanks for the comment! This is on the list to do, the material is not in shareable format, and we are working on ways to make it accessible. many thanks!

[@geinezhang7030]

quantpie hi,can let us know your background like what u do and how u know so much math?

[@jorgenberrenstein7575]

thank you

[@Eagle-eyed978]

Nice

[@ColocasiaCorm]

Which is fair because he's doing all the work. LOL

[@jaimecaballer1625]

real lol