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. So that was the formalism that I was very comfortable with and possibly even conditioned on due to my previous training in physics. So to reiterate, most of systems we analyze in physics are systems where time is continuous. Now, in finance, the situation is fundamentally different. Time is measured in discrete units, seconds, minutes, days, and so on. But in most of quantitative finance models, including the Black-Scholes model, time is continuous. So why is it choosing continuous? The answer that I can offer is that it's because continuous time formulation of dynamic system is in some way simpler, at least mathematically, than a discrete type formulation. A second possible reason is that as Mr. Soares said, these theories are modeled after Newtonian physics or physics in general, where time is usually continuous. So we said that closing a continuous time formulation, choosing continuous time formulation simplify analysis. And this is indeed the case in physics, typically, but is it true in finance? Is it true for option pricing in particular? Well, the Black–Scholes equation is analytically solvable only for a handful of options, including European puts and calls, binary options and a few others. But for all other options, numerical schemes are required, and all these numerical schemes use time discretization. So now we have also to worry about how our time discretized model for numerical implementation introduces errors due to time discretization. But why do we do all this? We just said that time is fundamentally discrete and final, so unlike in physics why they don't we work in a discrete time from the start? For options, proper units would be minutes, days, months and so on. If we state with a discrete time formulation, we do not have to worry about errors introduced by time discretization because this error is now zero because we are in a discrete time from the start. Yet on the other hand, formulation over discrete times, the caste system has a fundamental formulation somehow can also be perceived as somewhat too drastic. And this is because it also means that we do not have our beloved partial differential equations anymore. Now if 19 years ago when I just learned all these, someone would tell me that we can do better without PDEs than with them, I would now no doubt respond in disbelief. Doing option pricing without a model and even without a PDE, would sound back then as a kind of scientific heresy or maybe a modern day Luddites. And indeed some of the thoughts that I came up with when trying to interpret my formulas went so much against my perceived convictions as a theoretical physicist that it forced me to think again about what these connections in fact are or should be. And also about what physics as a science brings to finance, and how it all interacts with enforcement learning.