This blog will cover what is known as the “loss development triangle” (or insurance claims triangle). Last time I explained how investment funds work. If you haven’t read the article, please do so, it’s an interesting read for anyone that is curious about investing money.

The loss triangle is best described as a statistical instrument, which actuaries utilize (mathematicians specialized in risk issues – often insurance related). I will show you how this example is perfect for predictive 3D analysis by recognizing patterns.

What is the claims triangle used for?

This article explains the claims triangle and gives an example. Although it is about SQL, the author does a better job at explaining claims triangles than most. “The claims triangle is a way of reporting claims as they develop over a period of time.” Large insurance claims usually don’t get paid out right away but are spread out over multiple years. To understand the lingering effects of these payouts the claims triangle was invented.

Why is it called a claims triangle?

So why do we call it a claims triangle? That’s quite simple: we don’t have the data for the recent years yet. Claims made ten years ago, have had ten years to mature. For claims made five years ago, only five years of data will be available. This means the range of data is smaller the newer the claim is. This cumulative data forms the shape of a triangle when inserted into a table as this image shows. As you can see below the year of the claim is known, as is the years after the claim. In this example the blue numbers represent the last known payouts for each year. For 2016, only the initial payouts for that year are known. But the claims from 2010 have six years worth of data available.

What is the purpose of the claims triangle?

The purpose of the claims triangle is to predict the future. Everyone would love to know the future, right? Well, by using statistical equations we can predict the future with moderate certainty, which is better than remaining in the dark. But wouldn’t you agree that in its current form the data is hard to interpret? You can’t see the patterns in this table. This is too difficult for most people.

Using VRBI to generate a 3D claims triangle

The solution is to enter the data into the VRBI generator and create a 3D graph. The author of the SAP article used a dataset and we decided to turn it into a (fully rotatable) spatial graph. The table below contains the original data.


Entering the data in VRBI creates a 3D graph. The initial year of the claim is used as the X-value, the size of the claim as the Y-value and the amount of years from the initial claim as the Z-value. Sphere size is set to 2. Labels are added to clarify the years. We didn’t do this for the monetary values to keep things clear. We want to analyze patterns in this example. Each claim year has a different sphere color.

The graph output is in HTML, so you can view the real graph in your browser by clicking it! To experience the full power of VRBI – try clicking and dragging your mouse around to rotate and tilt the graph. Right-clicking and dragging results in moving the graph (translating). Refresh the webpage (F5) to return to the starting position.


Analysis of the 3D graph

Here we present few images from different perspectives, including some commentary.

claims triangle 3D graph 1The initial claims rise yearly. This could be because the company is growing. More customers mean more income but also results in more claims being made. The lines of the cumulative claims are also rising. This is because the payments continue to increase until the claim is completed years later. Therefore, the curves are seen bending downwards – clearly seen for 2005 and 2006.

claims triangle 3D graph 2
Something strange hits the eye from this angle: while the purple spheres show a normal increase, there are two abnormalities visible:

The last red sphere, as well as the brown one, jump upward. An explanation for this could be that the claims were higher or that they were paid out quicker.

claims triangle 3D graph 3
When viewing from yet another angle, it seems that the process is becoming more difficult each year. The curves are getting steeper in recent years, unlike in 2005 and 2006, which tend to smooth out near the end. This could be an indicator for rising costs in the future! An actuary would know this from calculations, but using 3D makes perfect sense for most people. We are visual beings after all.

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