Reinsurance as a Loss Transformation

Inflation and Layer Erosion

Separate claims inflation from exposure and mix, then test fixed and indexed reinsurance layers.

Inflation and Layer Erosion

Claims inflation changes both loss projections and which losses enter a nominal reinsurance layer. It can reflect repair prices, wages, medical costs, litigation, social attitudes, supply constraints, policy terms, and portfolio mix.

1. Put losses on a common level

If base-period loss is $X_0$ and cumulative severity index is $b_t$ ,

X_t=b_tX_0, \qquad b_t=\prod_{s=1}^{t}(1+i_s).

At constant annual inflation $i$ , $b_t=(1+i)^t$ . With 10% inflation, a £80,000 base loss becomes

80{,}000(1.10)^2=£96{,}800

after two years—not £96,000, because inflation compounds.

2. Fixed nominal layers erode

For a fixed attachment $a$ and limit $l$ ,

C_t=\min\{(b_tX_0-a)_+,l\}.

Consider £50,000 xs £50,000:

Time	Indexed loss	Ceded	Retained
base	£80,000	£30,000	£50,000
after two years at 10%	£96,800	£46,800	£50,000

More of the same real loss enters the fixed nominal layer. The reinsurer's expected frequency of attachment and expected recovery can rise even if the underlying real-risk distribution is unchanged.

Once loss exceeds £100,000, this layer is exhausted and further nominal inflation again falls on the insurer.

3. Indexed layers preserve a real position

If attachment and limit are indexed by the same $b_t$ ,

a_t=b_ta_0,\qquad l_t=b_tl_0,

then

\min\{(b_tX_0-b_ta_0)_+,b_tl_0\} =b_t\min\{(X_0-a_0)_+,l_0\}.

This preserves the layer in real terms under a common proportional inflation model. In practice, claim categories inflate differently and wording may index attachment, limit, or neither.

4. Separate four effects

Suppose observed average claim rises 15%. Decompose before applying a trend:

Effect	Example	Needed evidence
price/severity inflation	parts and labour cost more	matched claim categories and external indices
mix	more bodily injury, fewer glass claims	claim-type weights and within-type means
exposure	more or different vehicles insured	earned exposure and rating variables
settlement/reporting	claims close later or earlier	report, payment, and closure lags

An unsegmented mean cannot identify these mechanisms.

Composition example

If 90% ordinary claims average £2,000 and 10% complex claims average £20,000, portfolio mean is £3,800. If the complex share rises to 20%, mean becomes £5,600—a 47.4% increase with no inflation inside either group.

5. Inflation creates calendar effects in reserves

Claims paid in the same calendar year face similar repair and wage conditions even when they come from different accident years. In a run-off triangle, inflation can therefore align along diagonals.

A development-age-only chain ladder may absorb old inflation into its factors and project it forward implicitly. That can be too high or too low when inflation regime changes. Useful responses include:

bringing incremental claims to a common price level before fitting;
modelling origin, development, and calendar effects;
explicit severity trend scenarios;
separate treatment of large or long-settling claims.

Do not both pre-inflate data and add the same inflation again in future factors.

6. Stress the decision, not one parameter

For each plausible annual trend, recalculate:

gross ultimate losses and reserve;
attachment probability;
expected ceded loss;
probability of layer exhaustion;
net aggregate VaR/TVaR;
timing and reinstatement premium.

Stress	Gross effect	Fixed layer effect
uniform severity +10%	all losses scale	more attachment, possible exhaustion
only large losses +15%	centre may barely move	high layers change materially
faster settlement	payment timing changes	cash/recovery timing changes
high-cost class weight rises	mixture shifts	attachment frequency can jump

7. Current evidence, used carefully

Recent UK motor and liability publications document persistent concern about repair, wage, injury, and social inflation. They are useful external scenarios, but not plug-in parameters for Harbour Mutual:

ABI's motor claims-inflation discussion reports that its selected motor claims-cost measure grew faster than CPI over 2019–2023; it is an industry-authored summary with its own scope.
CAS research examines liability insurance inflation through year-end 2024 and emphasises line- and environment-specific effects.
ABI's 2025 payout release explicitly warns that improved data coverage limits direct absolute year-on-year comparison.

The defensible use is to create and document scenarios, then calibrate with portfolio data.

Practice

Inflate £120,000 for three years at 6% annually.
Under £100,000 xs £50,000, find ceded loss for £80,000, £120,000, and £190,000.
Why can a general consumer-price index be a poor claims index?

Answers

$120{,}000(1.06)^3\approx£142{,}922$ .
£30,000; £70,000; and £100,000 (the layer limit), respectively.
Claim baskets include specialised labour, parts, medical care, litigation, and mix effects whose weights and trends differ from household consumption.

Sources and further reading

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