Loss Ratio Distribution Modelling for the Business Plan
By Jonas Mohamed Osman Abdelghafour
Constructing a credible loss ratio distribution for the planning year, including rate adequacy, mix change and parameter uncertainty.
Executive answer
The planning-year loss ratio distribution is the core output of premium risk modelling. Its credibility depends less on the choice of distributional family than on whether the historical loss ratios used to fit it have been properly adjusted to today's rate level, mix and claims environment.
Parameter uncertainty is not optional
Fitting a distribution to eight or ten on-levelled loss ratios and treating the fitted parameters as known materially understates volatility. Parameter uncertainty should be propagated, typically through a Bayesian posterior or a bootstrap of the fitting process, and its contribution reported separately so its size is visible.
Cycle and dependence
Underwriting-cycle effects create autocorrelation across years and dependence across classes that a naive independent fit will miss. Modelling a common cycle factor, even a simple one, usually produces a more realistic aggregate distribution than adding correlation to the outputs after the fact.
Governance considerations
The distribution should be reconciled to the plan: the modelled mean loss ratio and the planned loss ratio should either agree or the difference should be explained. An unexplained gap normally means the plan is optimistic or the model is stale.
Conclusion
A loss ratio distribution earns its place when the underwriting team recognises the story it tells. If it is unrecognisable to them, the data adjustments are usually the reason.
Primary sources
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