Abstract
Insurance companies use conservative first order valuation bases to calculate insurance premiums and reserves. These valuation bases have a significant impact on the insurer’s solvency and on the premiums of the insurance products. Safety margins for systematic biometric and financial risk are in practice typically chosen as time-constant percentages on top of the best estimate transition intensities. We develop a risk-oriented method for the allocation of a total safety margin to the single safety margins at each point in time and each state. In a case study, we demonstrate the suitability of the proposed method in different frameworks. The results show that the traditional method yields an unwanted variability of the safety level with respect to time, whereas the variability can be significantly reduced by the new method. Furthermore, the case study supports the German 60 percent rule for the technical interest rate.
Highlights
Before the current low-interest period, the interest surplus often dominated all other surplus sources of insurance companies such that, in particular, the surplus from the biometric risk was considered to be negligible
We propose a sophisticated method for the calculation of a first order valuation basis with respect to the systematic biometric risk and the interest rate risk
The paper proposes a risk-oriented method for the allocation of the total safety margin to different points in time and transitions
Summary
Before the current low-interest period, the interest surplus often dominated all other surplus sources of insurance companies such that, in particular, the surplus from the biometric risk was considered to be negligible. We propose a sophisticated method for the calculation of a first order valuation basis with respect to the systematic biometric risk and the interest rate risk. Essential for this calculation is the decomposition of the total reserve according to the different risk sources. The main contribution of our paper is the derivation of an allocation method for the total safety margin to the different risk sources and different points in time. This is done in a joint framework for biometric and interest rate risk.
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