And here I want to start with asking the similar question to

one asked by Ben Dagoda.

Where do we stand today after the groundbreaking work of

Black-Scholes-Merton of 1973 on option price in modelling?

Since their work, thousands of papers have been written addressing different problems

with this age known theory.

But the fact of life is that it's still after all this efforts a dominant

model in both the industry and the academia.

And in this lecture, I will like to talk about ideas and methods from both physics

and the enforcement learning that can offer new ways for this very classical and

fundamental problems of quantitative finance.

So I want to talk about this very model that was the first thing I

learned about finance about 19 years ago when I decided to look for

a job in finance after finding myself, after two post docs in physics without

a clear perspective to find a faculty job in physics anywhere any time soon.

And presumably,

one of the first things I learned about quantitative finance is that it's mostly

about solving a diffusion equation under different boundary conditions.

And about the same time, econophysics has emerged.

And I started to read papers of Jean-Philippe Bouchaud, Eugene Stanley and

other econophysicists who started to apply new methods and

ideas from statistical physics to financial markets.

So given all that, I thought that

going to finance is not the worst thing that can happen to a physicist.

And then I started to look for other sources and

found books on Option Pricing by Paul Wilmott, an applied

mathematician who used the approach of partial differential equations or PDEs

to explain the Black-Scholes model and derive their surprising schemes.