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

Alessandro Ferriero

Abstract

Quantitative risk management for non-life insurance risk deals with a vector of random variables X₁,...,X_n (which represent the losses of different portfolios), its aggregated position S := X₁ + ··· + X_n, and a risk measure ρ(S) that quantifies the aggregated risk. The dependence between the X_i, 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.