 Hi everyone and welcome to part three of Actuarial History. Today we're talking about Abraham DeMove, the actuary who predicted his own death. Now the 17th century is crazy. We've got the globalization of trade, the establishment of the Bank of England and the birth of the formal stock market and private insurance companies. But with no entries, contracturations were short, it was more gambling rather than risk evaluation, lots of fraud and speculation, basically financial chaos. Now we saw in the last video that Casper Newman collected mortality data on a small European town. Thus it wasn't distorted by migration like the London mortality data. Now Casper Newman sends the data to Leibniz, always mispronouncing his name, who wasn't really that interested in it. So the data ends up with Edmund Haley and he uses his mathematical magic to price annuities based on a person's age. But the maths does start to get a little bit too difficult and he admits that he failed to handle more complex life assurance problems. So a quick little summary of the story so far. We've got Edmund Haley who's pricing annuities using mortality data. We've talked about James Dodson who wanted to form an insurance company based on actuarial science. Edmund Murs says that we need an actuary to do the calculations. He comes up with the name Actuary and then we see that we have someone called Richard Price who does the calculations and he mentors a young William Morgan who would go on to become the father of actuarial science. But let's look a little bit at Dodson because besides the finance of Richard Price he needed three things. The mathematics of Newton, the demography of Haley and the statistics of the star of today's video, Abraham D'Amove. Now funny enough all three of them were best friends and we can think of them as the three musketeers of actuarial science. Now Edmund Haley was a rich kid who sailed around the world, measured the solar system and basically had his bum in the butter. Abraham D'Amove was a little bit different. He got kicked out of France for being a Protestant and wasn't allowed to teach at English universities because he was French. And he was basically poor and alone. Well not really alone because he used to love to play chess at the cafes and he used to teach people how to gamble and he would tutor a lot of students. I mean there's one story about how he would tear up Isaac Newton's books so that he could read it while he was walking to his next student. But now if you thought that Isaac Newton was clever, Abraham was even smarter. And I mean this makes sense. In the Bible we see that it's father Abraham and you know he's got the son Isaac and even Isaac himself admitted that Abraham knows all these things better than I do. So I mean sorry I couldn't resist the little bit of a joke but I mean let's maybe prove this like why was Abraham smarter? Well Isaac Newton figured out the binomial theorem whereas Abraham was able to extend it to the multinomial theorem. And of course when the royal society heard about this they were like welcome to the club. Now look he did do quite a lot of cool stuff with planetary motion and saw a connection between trigonometry and complex numbers which I don't really understand so we're going to focus more on the statistical achievements and yeah let's go through some of them. The Poisson distribution. It wasn't Simon Denis Poisson but Abraham de Moeuf. The Gaussian distribution wasn't Carl Frederick Gauss but it was Abraham de Moeuf. I mean have you ever wondered why there is pi in the normal distribution formula? Well one day de Moeuf sat down and started flipping a bunch of coins and he was counting them over and over again. Now this lets him stumble on the central limit theorem which is probably the most important theorem in all of science and mathematics. I mean Alan Turing also kind of like figured it out or did the proof. Unfortunately a Scandinavian mathematician called Lindenburg had finished it before him. But coming back to pi what happens is Abraham's busy flipping the coins and he notices that n factorial is equal to the following expression. And he gets a little bit of assistance but he sees that this constant c is equal to the square root of 2 pi. Now if we had to look at the two formulas we can see with the binomial we have n factorial but when we come to the normal distribution we no longer have n factorial because we can use this approximation which incorporates pi. He was also the first to show moment generating functions and these magical mathematical formula allow you to calculate all the moments of a distribution. And you can learn more about these statistical things in my Udemy course on mathematical statistics for the actuarial exams and it's amazing to see how much of this is based on the work of Abraham de Moeve. So that's why when Hailey was you know complaining that oh my gosh the maths is too difficult Abraham de Moeve was able to come in and save the day. Now Edmund Hailey had written the following article an estimate of the degrees of mortality of mankind drawn from the curious tables of the births and funerals at the city of Brozlo with an attempt to assain the price of annuities upon lives. You can see he didn't have a publisher who's like you know maybe we need to work on it on a smaller title. Anyway he creates this this piece of work and it allows people to calculate you know life expectancy for two or three lives. But just how Abraham had extended Newton's binomial theorem to multi-nomial theorem he does the same with Hailey and allows the calculations to be done on multiple lives. Now a little bit of a heads up it wasn't perfect it was a little bit of an approximation but he does build on the work from Hailey and uses the table that Hailey had used. Now when we look at the the writings of James Dodson we see that he talks quite a lot about Abraham DeMove and the tables that he's now extended for the annuities for lives. And we see Richard Price himself also talking about Dr Hailey's observations and how it had been perfected by DeMove. William Morgan however was a little bit more critical of the approximation techniques used by DeMove and he made them a lot more accurate and that's probably why he's considered the father of actuarial signs and not Abraham DeMove. So in summary we have the following. Edmund Hailey he calculates the life expectancy for a few lives. Abraham DeMove he calculates the life expectancy for many lives although it is an approximation. James Dodson he builds an insurance company from this or says this is how it could be done. Richard Price is the person who actually does a lot of the earlier calculations for equitable life and then William Morgan improves the accuracy of the calculations. And what's quite nice is that Edmund and Abraham were friends. James Dodson was a student of Abraham. Richard Price worked for the company that James Dodson envisioned and then he himself tutored William Morgan. So it's quite nice how they're all kind of connected but let's talk about the myth. Let's end off with this actuary who predicted his own death. So it turns out Abraham DeMove he's observing you know the time he spends sleeping and he notices that it's increasing 15 minutes every single night. So he does a little bit of arithmetic progression and he realizes that this will increase until he's sleeping 24 hours on the 27th of November 1754. And he kind of thinks if I'm going to be sleeping constantly then that is probably the day that I'm going to die. And yeah he was right. So he accurately predicted the day of his death although not all historians agree on the story hence why we are going to put it as a myth rather than as factual truth. But yeah this is the end of part three but guys please like and subscribe if you want to see part four because there is still so much more to be told about the grand actuarial narrative and the history of this amazing subject. Make sure you check out part one as well as part two if you haven't already and as always have a great day. Cheers!