Pricing ambiguity in catastrophe risk insurance


Ambiguity about the probability of loss is a salient feature of catastrophe risk insurance, where historical loss data are limited. Hurricane insurance is a prominent example. Evidence shows that insurers charge higher premiums under ambiguity – that is, where there is uncertainty about the relative likelihood of events. However, in doing so they rely on simple heuristics, rather than being able to turn to pricing tools that formally link ambiguity with the insurer’s underlying economic objective.

The authors of this paper apply a newly developed insurance pricing model to two catastrophe model data sets relating to hurricane risk in two locations in the Atlantic basin. The model considers an insurer who maximises expected profit but is sensitive to how ambiguity affects its risk of ruin.

The authors estimate ambiguity loads – i.e. the extra insurance premium due to ambiguity – and show how these depend on the insurer’s attitude to ambiguity. They also compare these results with those derived from applying model-blending techniques, which have recently gained popularity in the actuarial profession, and show that model blending can lead to the counterintuitive result that the insurer prices catastrophe risk contracts as if it seeks ambiguity.

Key points for decision-makers

  • The authors applied an ‘alpha-maxmin’ model recently proposed by Dietz and Walker (2019) to two data sets, where conflicting catastrophe models create ambiguity about the probability of insured losses. The data sets both relate to hurricane risk in the Atlantic basin – one from Florida and the other from Dominica.
  • The authors demonstrate the practical use of the ‘alpha-maxmin’ model, an economic premium principle that treats ambiguity explicitly and thereby quantifies the ambiguity load as a function of the insurer’s attitude to ambiguity. They argue that applying this principle has the capacity to improve on ad hoc adjustments, even if this does not entirely negate the need for such adjustments.
  • The authors also compare the results from applying the ‘alpha-maxmin’ model with the premiums that would be quoted by an insurer applying popular model-blending techniques. The counterintuitive result is that these model-blending techniques can sometimes be inconsistent with insurer ambiguity aversion, implying the insurer is seeking ambiguity.

This version of the paper updates a previous version published in May 2019.