The term exposure inflation can refer to a couple of different phenomena within insurance. A friend mentioned a couple of weeks ago that he was looking up the term in the context of pricing a property cat layer and he stumbled on one of my blog posts where I use the term. Apparently my blog post was one of the top search results, and there wasn’t really much other useful info, but I was actually talking about a different type of exposure inflation, so it wasn’t really helpful for him.
So as a public service announcement, for all those people Googling the term in the future, here are my thoughts on two types of exposure inflation:
In which we correct our label encoding method from last time, try out a new algorithm - Gradient Boosted Regression - and finally managed to improve our score (by quite a lot it turns out)
An Actuary learns Machine Learning - Part 9 - Cross Validation / Label Encoding / Feature Engineering
In which we set up K-fold Cross Validation to assess model performance, spend quite a while tweaking our model, use hyper-parameter tuning, but then end up not actually improving our model.
An Actuary learns Machine Learning - Part 8 - Data Cleaning / more Null Values / more Random Forests
In which we deal with those pesky null values, add additional variables to our Random Forest model, but only actually improve our score by a marginal amount.
In which we plot an excessive number of graphs, fix our problems with null values, re-run our algorithm, and significantly improve our accuracy.
In which we start a new Kaggle challenge, try out a new Python IDE, build our first regression model, but most importantly - make these blog posts look much cleaner.
In which we take our final stab at the titanic challenge by ‘throwing the kitchen sink’ at the problem, setting up another 5 different machine learning models and seeing if they improve our performance (hint they do not, but hopefully it's still interesting)
In which we do more data exploration, find and then fix a mistake in our previous model, spend some time on feature engineering, and manage to set a new high-score.
An Actuary learns Machine Learning – Part 3 – Automatic testing/feature importance/K-fold cross validation
In which we don’t actually improve our model but we do improve our workflow - being able to check our test score ourselves, analysing the importance of each variable using an algorithm, and then using an algorithm to select the best hyper-parameters
In which we build our first machine learning model in Python, beat our previous Excel model on our first attempt, and then fail multiple time to improve this new model…
In which we enter a machine learning competition, predict who survived the titanic, build an Excel model, and then realise it performs no better than Kaggle’s ‘test submission’...
I sometimes get emails from individuals who have stumbled across my website and have questions about Lloyd's of London which they can't find the answers to online. Below I've collated some of these questions and my responses, plus some extra questions chucked in which I thought might be helpful.
A brief caveat - while I've had a fair amount of interaction with Lloyd's syndicates over the years, I have never actually worked within Lloyd's for a syndicate, and these answers below just represent my understanding and my personal view, other views do exist! If you disagree with anything, or if you think anything below is incorrect please let me know!
Are Lloyd’s of London and Lloyds bank related at all?
They are not, they just happen to have a similar name. Lloyd’s of London is an insurance market, whereas Lloyd’s bank is a bank. They were both set up by people with the surname Lloyd - Lloyds bank was formed by John Taylor and Sampson Lloyd, Lloyd’s of London by Edward Lloyd. Perhaps in the mists of time those two were distantly related but that’s about it for a link.
I just finished reading ‘I am a strange loop’ by Douglas Hofstadter, and before I say anything else about the book, I’ll say that I really did want to like it.
I’m a huge fan of his better known book ‘Godel, Escher, Bach’ for which Hofstadter won a Pulitzer Prize, I’m also very interested in the subject area – maths, logic, self-reference, cognitive science. However there were just too many things that rubbed me up the wrong way, in no particular order here were all the things I didn’t like about the book:
I had to solve an interesting problem yesterday relating to pricing an excess layer which was contained in another layer which we knew the price for – I didn’t price the initial layer, and I did not have a gross loss model. All I had to go on was the overall price and a severity curve which I thought was reasonably accurate. The specific layers in this case were a 9m xs 1m, and I was interested in what we would charge for a 6m xs 4m.
Just to put some concrete numbers to this, let’s say the 9m xs 1m cost \$10m
The xs 1m severity curve was as follows:
Let me introduce a game – I keep flipping a coin and you have to guess whether it will come up heads or tails. The prize pot starts at \$2, and each time you guess correctly the prize pot doubles, we keep playing until you eventually guess incorrectly at which point you get whatever has accumulated in the prize pot.
So if you guess wrong on the first flip, you just get the \$2. If you guess wrong on the second flip you get \$4, and if you get it wrong on the 10th flip you get \$1024.
Knowing this, how much would you pay to enter this game?
You're guaranteed to win at least \$2, so you'd obviously pay at least $\2. There is a 50% chance you'll win \$4, a 25% chance you'll win \$8, a 12.5% chance you'll win \$16, and so on. Knowing this maybe you'd pay \$5 to play - you'll probably lose money but there's a decent chance you'll make quite a bit more than \$5.
Perhaps you take a more mathematical approach than this. You might reason as follows – ‘I’m a rational person therefore as any good rational person should, I will calculate the expected value of playing the game, this is the maximum I should be willing to play the game’. This however is the crux of the problem and the source of the paradox, most people do not really value the game that highly – when asked they’d pay somewhere between \$2-\$10 to play it, and yet the expected value of the game is infinite....
The above is a lovely photo I found of St Petersburg. The reason the paradox is named after St Petersburg actually has nothing to do with the game itself, but is due to an early article published by Daniel Bernoulli in a St Petersburg journal. As an aside, having just finished the book A Gentleman in Moscow by Amor Towles (which I loved and would thoroughly recommend) I'm curious to visit Moscow and St Petersburg one day.
I work as a pricing actuary at a reinsurer in London.