Actuarial Geometry

The literature on capital allocation is biased towards an asset modeling framework rather than an actuarial framework. The asset modeling framework leads to the proliferation of inappropriate assumptions about the effect of insurance line of business growth on aggregate loss distributions. This paper explains why an actuarial analog of the asset volume/return model should be based on a Lévy process. It discusses the impact of different loss models on marginal capital allocations. It shows that Lévy process-based models provide a better fit to the NAIC annual statement data. Finally, it shows the NAIC data suggest a surprising result regarding the form of insurance parameter risk. Keywords: Capital determination, capital allocation, risk measure, game theory, Lévy process, parameter risk, diversification.