Actuarial pricing, capital modelling and reserving

Pricing Squad

Issue 24 -- May 2018

Welcome to Pricing Squad

Pricing Squad is the newsletter for fellow pricing practitioners and actuaries in general insurance.

Today's issue starts in a B-52 bomber.

How to find exposure concentrations (or detonate a bomb)

The picture that is worth a thousand words:

So how well do you understand geographical risk cumulations in your book?

Can you identify them correctly or do you rely on a simplified "what else is within a given radius of each risk" algorithm? A simplified algorithm would not flag the concentration pictured above. But the picture represents a common situation in busy ports of China and in urban centres around the world.

The proper algorithm for finding such concentrations used to be called "the bomb problem". These days you need to Google for "algorithm to cover maximal number of points with one circle of given radius" instead. Language is just not what it used to be...

The algorithm analyses each pair of exposure points, encircles them with two different maximal circles, then finds other points caught by those circles. The entire process has computational complexity of O(N^3) but can be reduced to O(N^2 log(N)).

Since locations on planet Earth are described in latitude and longitude, implementing the bomb problem will be a refresher in linear algebra for any brave soul.

For everyone else, the bomb problem is now a part of the free ProInsurance add-in for Excel, just click the "Bomb" tool.

Let me know in case you need your own user account for downloading.

Copyright © 2018 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.