Actuarial pricing, capital modelling and reserving

Pricing Squad

Issue 29 -- January 2019

Welcome back in 2019!

Pricing Squad is the newsletter for fellow pricing practitioners and actuaries in general insurance. Today's issue is about things that follow Pareto distribution.

Things that follow Pareto distribution

Did you notice how insanely unequal things are in nature?

Nearly the entire universe is vacuum but a few points are unimaginably dense black holes.

The world frequently follows the strangely ubiquitous Pareto distribution. Here are some such items: size of human settlements, values of natural oil reserves, size of meteorites, clusters of Bose-Einstein condensate near absolute zero, runtime of computer programs, economic success of humans and businesses and finally, insurance claims.

Do your large losses follow a Pareto distribution? For me, 9 out of 10 times the answers is "yes".

Here is how you can check your account.

First, derive the empirical probability function for losses above a threshold, say $10m.

Then plot the tail of the empirical cumulative distribution function on a log-log scale like this:

The log-log scale is essential because it brings up the hidden linearity of extreme events.

If the empirical points follow a straight line then you can probably assume a Pareto distribution. Also, Pareto alpha = -slope of the trend.

Once you know the exact Pareto distribution, you can extrapolate limited experience into truly extreme territory. For example you can derive technical price for any layer of XoL business or calculate large loss loads for personal lines. You can even modify the slope parameter using expert judgement.

Let me know if you find this useful for your book of business!

Copyright © 2019 Jan Iwanik, All rights reserved. You are receiving this email because you subscribed to updates from We publish data and analysis for informational and educational purposes only. You can unsubscribe from this list by emailing us.