Journal of Risk

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How to build a risk factor model for non-life insurance risk

Alessandro Ferriero

  • In this paper we present a dependence model for non-life insurance risk based on risk factors, analogous to those generally used for life insurance or asset risk.
  • The main advantages of our model are the ability to capture the essential mechanisms behind the dependencies; the possibility of quantifying the contribution of a risk factor to the total risk of the portfolio; and the flexibility to model different type of dependencies, including nonsymmetric and multidimensional structures which cannot be modelled with Clayton, Gumbel or Gauss copulas.

Quantitative risk management for non-life insurance risk deals with a vector of random variables X1,...,Xn (which represent the losses of different portfolios), its aggregated position S := X1 + ··· + Xn, and a risk measure ρ(S) that quantifies the aggregated risk. The dependence between the Xi, i ⊆ 1,...,n, and how it is modeled is crucial because this has a large effect on the aggregated position S and thus on the aggregated risk ρ(S). In this paper we present a dependence model for non-life insurance risk based on risk factors, analogous to those generally used for life insurance or asset risk. In practice, however, it is cumbersome to build this type of model for non-life insurance risk for two main reasons. First, most of the risk factors are difficult to model, and second, the relation between risk factors and losses is complex to determine. Here, we propose a method to bypass these difficulties.

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