The average cost per claim method: Estimating P&C loss reserves in an inflationary environment

As actuaries, we rely on historical patterns to project future insurance claim payments. But sometimes, those patterns can change in ways that make traditional development factor approaches unsuitable. The recent spike in inflation is a dramatic example of this. Chain-ladder methods can handle periods of stable inflation, but when inflation levels fluctuate, we need to look further afield.

Fortunately, there are tools at our disposal that allow us to handle these types of changes. The average cost per claim (ACPC) method is one such tool. Since it concentrates on incremental instead of cumulative payments, it allows us to deal with situations where inflation is variable rather than a constant. And it can also account for different possible assumptions about future inflation.

The method

The ACPC method relies on two assumptions:

• Claims are paid when claims are closed.
• Average claim costs vary by the development period in which they are closed.

To calculate future claims payments, ACPC simply takes the number of expected future closed claims (in each future development period for each accident period) multiplied by the average cost for each corresponding development period (Figure 1).

Figure 1. The ACPC method to calculate future claims payments

The ACPC method to calculate future claims payments

Simple, right? But too simple.

• What if we know that the average costs are different for different accident periods (as they were during COVID-19)?
• Or what if we know that inflation is impacting average costs by calendar period and that they are going to be even higher going forward due to excess inflation?

This is where the ACPC method really shines. To handle accident-period fluctuations, it allows us to enter accident-period adjustment factors to get our historical average claim costs on a more comparable basis. In this case, we are assuming that accident year 2020 average payments are 50% of the other accident years, so we are doubling those average payments to make them comparable. Then, we can further adjust our average claim costs to account for historical calendar-period inflation to bring the average payments up to the current level (Figure 2).

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This historical inflation can be calculated by fitting curves to our data, using industry factors or taking some combination of the two.

Once we have comparable historical average claim costs, we can select an average claim cost for each development period. This gives us the preliminary future expected average claim costs by development period. We can then reflect the accident-period adjustment factors and apply future calendar-period inflation to arrive at the average cost per claim in each future development period for each accident period. We can then multiply these expected future average claim payments by the expected future closed claims (for each accident period and development period) to generate unpaid losses.

Caveats

The ACPC method has limitations that make it inappropriate for some lines of business and in certain situations:

• Since the ACPC method assumes that payments are made when claims are closed, it may not be appropriate when there are partial payments or reopened claims.
• It also assumes that average payment levels (after adjusting for accident period fluctuations and inflation) are consistent within each development period. Delays or acceleration of claim closure rates may affect this.
• Additionally, this method assumes that average claim payment levels are impacted by calendar-period inflation when the claim is paid, not just when the claim occurs.

Final thoughts

For actuaries, there is no one way to deal with changing economic conditions while making projections. Having additional tools can enable us to make better-informed decisions. While the ACPC method makes some simplifying assumptions, it is an elegant and straightforward method for incorporating changing levels of inflation.

Also, it’s another fun acronym to add to our repertoire. Who doesn’t love that?