Ergodic Exploration in Finance

[@TheUndergraduateQuant]

This is gold! Thx always for your content! A must watch!

[@amj864]

Interesting way of thinking

[@scottlanigan]

Great video! Would you still recommend the books linked in the bio for learning more about ergodic theory? I've been reading a lot of Taleb, Peters, and others but would like the definitive "go-to" book on this.

[@DimitriBianco]

It depends on your background. I still like Einsiedler and Ward's book however it can be challenging to digest without a strong math background. I still have to look up other ideas as I have read through the book (I am not a mathematician by academic training).

[@DimitriBianco]

I also have not read Taleb or Peters so I can't really compare.

[@scottlanigan]

@@DimitriBianco Thanks!

[@jenpalex2]

If you are looking for new topics, here are a couple I would like to see. What do you think of the work stemming from Thomas Cover’s Universal Portfolio concept. This claims to work regardless of the statistical properties the price time series? Also anything you could do to make the statistical arguments in Nassim Taleb’s publications, such as ‘Statistical Connsequences of Fat Tails’ would be much appreciated

[@sambakker7563]

I have a question about 16:30 , why couldn’t this add up to 1 pdf which can be estimated by some non parametric way?

[@DimitriBianco]

You could try and model the distribution as one and it could be ergodic however there are often advantages in understanding the model in components. For example if one distributing is failing while the other is stable the specified model will often fail slower giving you time to rebuild the one curve. It also makes figuring out what specifically is wrong with the environment and model. Imagine you know (think) rates are going to continue to rise which will make the distribution change. You can adjust and stimulate in advance. If you had one curve that fit multiple distributions it might not logically change as expected.

[@DengueBurger]

I think Nicolas Nassim Taleb talks about Ergodicity. Like, one guy goes to a casino and plays till he goes bust, he can no longer keep playing. But if you have a bunch of casino players, they have an average earnings that is a lot more reliable. So basically, you don’t want to bet on those situations where you can go bust and never come back and go into those situations because you said “well the average casino player only goes bust after 50 hands of cards played, so I an individual should be fine as long as I don’t fly too close to 50 hands.” You want to avoid those critical bust situations and naively base things on the average of the collective. Similar things happen in financial markets.

[@Oscar-zp6io]

Amazing video! Even though I have very little knowledge about the topics discussed, I was able to understand most of it. Please keep videos like these coming

[@chidalunwaimo876]

There is a physicist who studies this in relation to the stock market "Dr Ole Peters"

[@rohansundar5227]

Hey quick question, feel free to ignore if it is dumb. What if we change the clock? What I mean is instead of the chronological sampling that most financial time series use, we could sample based on an event like say transactions or number of shares tested. For example we sample the price of AAPL when 500 AAPL shares are traded. So we no longer have a regular clock, we have a random clock. Would that series be ergodic?

[@DimitriBianco]

It would depend on the properties of Apple itself. Erodicity isn't necessarily time specific. Stationarity is time specific. For example, Russian Roulette isn't ergodic from an individual perspective as the probability doesn't converge. Now if you were viewing this from a large group perspective, it would be ergodic and converge.

[@rohansundar5227]

@@DimitriBianco thanks that's an important clarification, so a process can be stationary but non ergodic

[@Eta_Carinae__]

​@@rohansundar5227 For clarity, an ergodic process is defined to be one in which the time-series mean is identical to the cross-sectional mean. Think: a Lorentz attractor. It looks the same if you run many different points along it for a small amount of time as it does if you run one point around it for an extensive period of time. The means will consequently be the same. Stationarity is defined as the CDF of a joint distribution at some set of time-samples is independent of the CDF obtained by the distribution of samples shifted in time by any amount. Usually this implies the condition of mean and variance also being independent of time, and deseasonalised.

[@tharun2266]

Hello, My name is Tharun. I am a Junior in highschool and I have recently been interested in the Quant Finance Career path and I had a couple questions. 1. I am planning on Majoring in Computer Science and double Minoring in Applied Mathematics and Finance. I wasn't sure if this is the right path that I should take and if the course work will be too heavy or if I should consider double majoring instead, if so in what fields? 2. I wasn't sure if I should directly plan on completing my masters or if I should work for a couple years, if I don't decide to complete my masters right after my undergrad, what kind of jobs should I be looking for with my majors and what jobs should I be looking for to break into quant?

[@DimitriBianco]

Focus on the minimum and then see how much extra time the minors will add. I'm not a fan of work experience as there isn't a lot of it available for quant finance without the masters. Here is a video of my opinion on it. kzbin.info/www/bejne/oGacoWt7aNKCrNk

[@tharun2266]

@@DimitriBianco Thank you very much I just watched the video. One last question, what would say the minimum for a Quant is in undergrad? I feel like Computer Science, Applied Math, and Finance are all needed but I'm not sure which two fields to focus on if I had to.

[@DimitriBianco]

@@tharun2266 I'd focus on math and statistics. Most quant masters will require Calc 1-3, intro tp probability, ODE, and pde. I'd also recommend real analysis, intro to stats, and linear algebra.

[@6Ligma]

Dimitri when you want to model the first and second moment as "time dependant", you describe it as a summation of a drift and a weiner process, right?

[@DimitriBianco]

Using drift and a Weiner process is one way however many processes do not follow this structure. It works in option pricing for very specific conditions (Black-Scholes assumptions) however in practice things aren't so simple.

[@gabriellara7456]

Dimitri, could you make a video on your thoughts about the CQF institution and its certification? Its cost is quite spicy (especially for non USD earning professionals) but seems useful for aspiring quants.

[@brianferrell9454]

just subscribed

[@DimitriBianco]

Thanks!

[@arturoarellanoarias2373]

Hi Dimitri, nice video! Another book with an excellent exposition of Ergodic Theory from a perspective of dynamical systems is "Foundations of Ergodic Theory" by Marcelo Viana. It has plenty of problems with hints. In another regard, would you recommend paying for a program on Coursera? The one I am thinking about is the Financial Engineering and Risk Management Specialization offered by Columbia University.

[@spinLOL533]

i was shocked that i understood this video

[@cake_lynx]

I am a first year in a mixt economics/Cs degree, and the happiness from being able to follow along is unimaginable. Can't wait for my econometrics and quantitative economics courses next year

[@rosh6211]

Hey dimitri Can i get a goood quant role If i have a bcom in applied finance and analytics with honors and research. It had alot of financial modeling Applied econometrics Python R Statistics with r Applied buisness mathematics,statistics and economics I also am planning on a financial engineering certificate from Indian institute of quantitative finance

[@DimitriBianco]

It depends what country you are in for the ability to find work but educationally you'll be behind. Even with a grad degree there is a lot to learn.

[@rosh6211]

@@DimitriBianco what if i do bsc computer Science honors Online

[@ay5960]

Poincare recurrence is one my favorite theorems and also Hopf decomposition after that. The conservative part could be beneficial for statistical arbitrage. But not sure how plausible it is to assume that we can create algorithms which can perform these types of decompositions. Anyways great content I will be reading his work!