Case study on Loss Curves (Actuarial Science)

We just added a new case study:

Modelling Loss Curves in Insurance with RStan

Mick Cooney

Loss curves are a standard actuarial technique for helping insurance companies assess the amount of reserve capital they need to keep on hand to cover claims from a line of business. Claims made and reported for a given accounting period are tracked seperately over time. This enables the use of historical patterns of claim development to predict expected total claims for newer policies.

In insurance, depending on the types of risks, it can take many years for an insurer to learn the amount of liability incurred on policies written during any particular year. So, at a particular point in time after the policy is written some claims may not reported or known about by then, or some claims are still working through the legal system so the final amount due is not determined.

Total claim amounts from a simple accounting period are laid out in a single row of a table, each column showing the total claim amount after that period of time. Subsequent accounting periods have less development, so the data takes a triangular shape - hence the term ‘loss triangles’. Using previous patterns, data in the upper part of the triangle is used to predict values in the unknown lower triangle, giving the insurer a probabilistic forecast of the ultimate claim amounts to be paid for all business written.

The ChainLadder package provides functionality to generate and use these loss triangles.

In this case study, we take a related but different approach: we model the growth of the losses in each accounting period as an increasing function of time, and use the model to estimate the parameters which determine the shape and form of this growth. We also use the sampler to estimate the values of the “ultimate loss ratio”, i.e. the ratio of the total claims on an accounting period to the total premium received to write those policies. We treat each accounting period as a cohort.


I missed out on a few references that I would like to add to the case study.

I will add them tonight, would it be possible to get the updates added to the version on the website once that is done?

Sure. Easiest for us if you can create a pull request on the web site’s repo on stan-dev. But if you don’t know how to use GitHub, it’s probably not worth learning for this and I can do it for you.