Abstract
The quantitative requirements of Pillar One are supplemented by the qualitative requirements of Pillar Two. Thus, the Solvency II framework is not complete without considering qualitative requirements (Heep-Altiner et al. 2016, p. 10).
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Notes
- 1.
In contrast to risks being defined as negative deviations from expectations (on financial positions), chances are defined as positive deviations from expectations.
- 2.
Those topics will be treated in more detail in Sect. 4.1.
- 3.
Given a random variable X within [0, 1] and with EV [X] = p, then X 2 ≤ X und thus
$$ \mathrm{VAR}\ \left[\mathrm{X}\right]=\mathrm{EV}\left[{\mathrm{X}}^2\right]\hbox{--} \mathrm{EV}\ {\left[\mathrm{X}\right]}^2\le \mathrm{EV}\left[\mathrm{X}\right]\hbox{--} {\mathrm{p}}^2=\mathrm{p}\hbox{--} {\mathrm{p}}^2. $$The equation holds exactly for Bp.
- 4.
As explained before, the increase in the property volume would normally increase the own funds having an impact on the adjustment calculation. This double effect has not been taken into account.
- 5.
It should be noted that, in case of the internal model, the required capital has been defined by the capital distribution at the end of the year.
- 6.
As trademarked by Stern Stewart & Co.
- 7.
See the Sect. 2.1.1 on the IFRS revaluation of the available capital.
- 8.
See the chain ladder analysis in the Sect. 2.1.1 for the IFRS revaluation of the available capital.
- 9.
Even a combined ratio above 100% could imply profitable business if the corresponding negative technical result could be compensated regularly by the non-technical result in case of a high liquidity according to LoB with high durations.
- 10.
In this equation, RoL denotes the return on liquidity and C the last coupon from the level-coupon bond.
- 11.
For detailed information with respect to the standard formula, compare Sect. 2.2.
- 12.
The depreciation factor of 80.0% is pre-defined in the standard formula.
- 13.
Key performance indicators measure the company’s performance over a time interval. There are classic performance indicator, e.g. the return on capital (RoC), that are not linked to any risk measure or risk indicator. Although, in the context of risk control, only risk based performance indicator are relevant, the notation KPI will be kept unchanged because it is well established.
- 14.
The calculation of the adjustments has been explained in Sect. 2.2.4 and will, therefore, not be treated any longer.
- 15.
Changes in the risk profile should be detected by ORSA but there may be some time delay.
- 16.
Regarding the (pure value-based) indicator RoC, there does not exist a reasonable decomposition of the available capital in general.
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Heep-Altiner, M. et al. (2018). Application of the Data Model: Pillar Two. In: Heep-Altiner, M., Mullins, M., Rohlfs, T. (eds) Solvency II in the Insurance Industry. Contributions to Management Science. Springer, Cham. https://doi.org/10.1007/978-3-319-77060-4_3
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