Abstract
We study the dynamics of the one-year change in P&C insurance reserves estimation by analyzing the process that leads to the ultimate risk in the case of “fixed-sum” insurance contracts. The random variable ultimately is supposed to follow a binomial distribution. We compute explicitly various quantities of interest, in particular the Solvency Capital Requirement for one year change and the Risk Margin, using the characteristics of the underlying model. We then compare them with the same figures calculated with existing risk estimation methods. In particular, our study shows that standard methods (Merz–Wüthrich) can lead to materially incorrect results if the assumptions are not fulfilled. This is due to a multiplicative error assumption behind the standard methods, whereas our example has an additive error propagation as often happens in practice.
Highlights
In the new solvency regulations, companies are required to estimate their risk over one year and to compute a Risk Margin (RM) for the rest of the time until the ultimate risk margin is reached
The goal is to study the one year change required by the new risk based solvency regulations (Solvency II and the Swiss Solvency Test)
Merz–Wüthrich method and the COT method developed at SCOR
Summary
In the new solvency regulations, companies are required to estimate their risk over one year and to compute a Risk Margin (RM) for the rest of the time until the ultimate risk margin is reached. Actuaries are not accustomed to do so. Until recently, their task mostly consisted of estimating the ultimate claims and their risk. There are only very few actuarial methods that are designed to look at the risk over one year. Among the most popular ones is the approach proposed by Merz and Wüthrich (2008) as an extension of the Chain–Ladder following Mack’s assumptions (Mack 1993). They obtain an estimation of the mean square error of the one-year change based on the development of the reserve triangles using the Chain–Ladder method
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