@user-cr3vw7gj2i
The diffusion equation is originated using as assumption that the particles move in Brownian motion. The equation is obtained over the reasoning of the probability of getting in a particular point in space coming from different positions in the neighborhood of the final point. The solution of this differential equation is the pdf of the normal distribution. Another approach is trying to find the function that determines the number of particles located in position X in a rectangle of side dx. In this second case we find again the same differential equation with solution the pdf of the normal distribution. As you see in the first case we found the pdf to get to some point in the space and in the second case we found a function ( not a pdf) which tells you how many particles there are in a volume (area) in the space. This function is also a pdf of a normal distribution. So we have two ways, the first solve a differential equation to find a pdf and the second solve same equation to find a function that tells you number of particles. Which is also a pdf. Do you see my problem?. In both cases we don't get information about the size of the movement of the stock price. Wiener did focuses on that
@Tyokok
Thanks for the brilliant lecture! Two questions: 1) why here for Arithmetic Brownian Motion simulation you use the difference as return, as opposed to Geometric Brownian Motion (which using log return). What's the rational to use different as return here? If anyone knows please also advice, thank you! 2) instead of using N simulation paths, can we directly use T=50 to get pdf for T at 50th days, and generate N simulation, would that be the same? 3) we have to annualized the parameter estimate? GBM use continuous compound, but here ABM why need annualized parameter? Thank you!
@hamidrezamofidi3211
Amazing! Do you plan to make videos on Math neuroscience or Neural networks by any chance? That would be excellent if you do.
@duckymomo7935
This was so clear to follow Just hated the voice; I know in more recent vids you use a real voice
@schtefel
awesome work, my uni course is a bit whack, your videos allow me to understand what's going on! is the Excel file downloadable somewhere? Thanks a lot
@pkdeyiitkgp
Hi, Please can you share the presentation slides.
@guyw6701