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Speaker(s): Michael Fackler (independent actuary)
In (re)insurance premium rating, older loss data are often adjusted before the statistical evaluation by means of an "external" inflation index (calculated not from the data itself). By doing so, it is implicitly assumed that this index exactly reflects the inflation of the insured losses. However, in practice there should mostly be a slight deviation between the "true" loss inflation and the index.
We propose a stochastic approach for this "basis risk" and show how it changes the statistical properties of premium rating: fundamentally, but in accordance with intuition. In particular, older data becomes gradually less representative than recent data.
Then, a comprehensive model for the uncertainty of past and future inflation is developed, having at its heart a system of all types of inflation that matter for the rating. Finally, we show how to improve the forecast accuracy (mean squared error) of premium rating by appropriately weighting the data by age.
For this purpose, we propose a loss count model for risks/portfolios of variable size that describes the dependence of variance on volume very flexibly, filling the gap between two classical models: independence of the single insured objects versus strong dependency via a market-wide loss frequency fluctuation.
To embrace non-proportional risk transfer (deductibles, limits, layers), we develop an analytical theory for the generally non-linear, leveraged impact of inflation on the risk premium. We show how the leverage depends on the geometry of the loss severity cdf, quantifying it by a novel distribution parameter: the regional Pareto alpha.