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Inflation modelling - Nth largest - part 4 - percentiles

25/7/2023

 

In the last few posts I’ve been writing about deriving claims inflation using an ‘N-th largest loss’ method. The thought popped into my head after posting, that I’d made use of a normal approximation when thinking about a 95% confidence interval, when actually I already had the full Monte Carlo output, so could have just looked at the percentiles of the estimated inflation values directly. 

Below I amend the code slightly to just output this range directly.

Picture
Continuing my inflation theme, here is another cool balloon shot from João Marta Sanfins

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Inflation modelling - median of top 10 losses, with additional years of data

24/7/2023

 

In my last couple of post on estimating claims inflation, I’ve been writing about a method of deriving large loss inflation by looking at the median of the top X losses over time. You can read the previous posts here:

Part 1:  www.lewiswalsh.net/blog/backtesting-inflation-modelling-median-of-top-x-losses
Part 2: www.lewiswalsh.net/blog/inflation-modelling-median-of-top-10-losses-under-exposure-growth
​
One issue I alluded to is that the sampling error of the basic version of the method can often be so high as to basically make the method unusable. In this post I explore how this error varies with the number of years in our sample, and try to determine the point at which the method starts to become practical.
Picture
Photo by Jøn

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Inflation modelling - median of top 10 losses, under exposure growth

18/7/2023

 

I previously wrote a post in which I backtested a method of deriving large loss inflation directly from a large loss bordereux. This post is an extension of that work, so if you haven't already, it's probably worth going back and reading my original post. Relevant link:
www.lewiswalsh.net/blog/backtesting-inflation-modelling-median-of-top-x-losses
​
In the original post I slipped in the caveat that that the method is only unbiased if the underlying exposure doesn’t changed over the time period being analysed. Unfortunately for the basic method, that is quite a common situation, but never fear, there is an extension to deal with the case of changing exposure.

Below I’ve written up my notes on the extended method, which doesn't suffer from this issue. Just to note, the only other reference I’m aware of is from the following, but if I've missed anyone out, apologies! [1]
Picture
St Paul's, London. Photo by Anthony DELANOIX

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    ​​I work as an actuary and underwriter at a global reinsurer in London.

    I mainly write about Maths, Finance, and Technology.
    ​
    If you would like to get in touch, then feel free to send me an email at:

    ​[email protected]

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