An Approximation of the Non-Life Reserve Risk Distribution Using the Cornish-Fisher Expansion

In order to get more insights into the characteristics of the non-life reserve risk distribution, the Cornish-Fisher expansion model is used. For this model, the knowledge of the first four moments of the distribution is necessary. These moments are derived using closed-form formulas. For the first two moments, the results described in Mack 1993 are used. For the third and fourth moments, closed-form models are introduced.The proposed model is tested on 7 different triangles publicly available. It appears that the resulting distributions are different depending on the line of business but also on the (re)insurer. Therefore, it can be concluded that the knowledge of the characteristics of the reserve risk distribution can contribute to a better modelling of the reserve risk of each (re)insurer