Taking the One-Year Change from Another Angle
35 Pages Posted: 25 Jun 2016
Date Written: June 21, 2016
Abstract
We study the dynamics of the one-year change in P&C insurance reserves estimation by defining a simple but realistic process that leads to the ultimate. The random variable at ultimate 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 capital obtained with existing risk estimation methods. In particular, our study shows that if the assumptions on the process are misspecified, the traditional methods can lead to very wrong results. This is due to a multiplicative error assumption. Instead, our model assumes an additive error propagation as is often encountered in practice.
Keywords: one-year risk, stochastic process, chain ladder, Solvency II, Solvency Capital Requirement
JEL Classification: c15,c52,g22
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