I’ve had the textbook 'Modelling Extremal Events: For Insurance and Finance’ sat on my shelf for a while, and last week I finally got around to working through a couple of chapters. One thing I found interesting, just around how my own approach has developed over the years, is that even though it’s quite a maths heavy book my instinct was to immediately build some toy models and play around with the results. I recall earlier in my career, when I had just got out of a 4-year maths course, I was much more inclined to understand new topics via working through proofs step-by-step in long hand, pen to paper.
In case it’s of interest to others, I thought I’d upload my Excel version I built of the classic ruin process. In particular I was interested in how the Cramer-Lundberg theorem fails for sub-exponential distributions (which includes the very common Lognormal distribution). Therefore the Spreadsheet contains a comparison of this theorem against the correct answer, derived from monte carlo simulation.
The Speadsheet can be found here:
The first tab uses an exponential distribution, and the second uses a Lognormal distribution. Screenshot below.
I also coded a similar model in Python via Jupyter Notebook, which you can read about below.
I work as an actuary and underwriter at a global reinsurer in London.