Division Method specificationF1

For the purpose of paragraphs 4-7, the following notation shall apply:

1. (a)

   n denotes the number of financial years for which aggregated annual losses data is available;

2. (b)

   Y _i denotes the aggregated losses in financial year i ;

3. (c)

   μ and ω denote the first and second moment, respectively, of the aggregated annual losses distribution, being equal to the following amounts:

   • $\mu =\frac{1}{n}\sum _{i=1}^n{Y}_i$

     and

     $\omega =\frac{1}{n}\sum _{i=1}^n{Y}_2^i$

4. (d)

   b ₁ denotes the amount of the retention of the recognisable stop loss reinsurance contract referred to in Article 218(2);

5. (e)

   where the recognisable stop loss reinsurance contract referred to in Article 218(2) provides compensation only up to a specified limit, b ₂ denotes the amount of that limit.

The undertaking-specific specific adjustment factor for non-proportional reinsurance shall be equal to the following:

• NP _USP = c · NP′ + (1 – c ) · NP

where:

1. (a)

   c denotes the credibility factor set out in section G;

2. (b)

   NP′ denotes the estimated adjustment factor for non-proportional reinsurance set out in paragraph 5;

3. (c)

   NP denotes the adjustment factor for non-proportional reinsurance set out in Article 117(2).

The estimated adjustment factor for non-proportional reinsurance shall be equal to the following:

where the parameters μ ₁ , μ ₂ , ω ₁ and ω ₂ are set out in paragraph 6.

The parameters μ ₁ , μ ₂ , ω ₁ and ω ₂ shall be equal to the following:

• ${\mu }_1=\mu \times N\left(\frac{\ln \left(b_1-\theta \right)}{\eta }-\eta \right)+b_1\times N\left(-\frac{\ln \left(b_1\right)-\theta }{\eta }\right)$

• ${\mu }_2=\mu \times N\left(\frac{\ln \left(b_2-\theta \right)}{\eta }-\eta \right)+b_2\times N\left(-\frac{\ln \left(b_2\right)-\theta }{\eta }\right)$

• ${\omega }_1=\omega \times N\left(\frac{\ln \left(b_1-\theta \right)}{\eta }-2\times \eta \right)+b_2^1\times N\left(-\frac{\ln \left(b_1\right)-\theta }{\eta }\right)$

• ${\omega }_2=\omega \times N\left(\frac{\ln \left(b_2-\theta \right)}{\eta }-2\times \eta \right)+b_2^2\times N\left(-\frac{\ln \left(b_2\right)-\theta }{\eta }\right)$

where:

1. (a)

   N denotes the cumulative probability function of the normal distribution;

2. (b)

   ln denotes the natural logarithm;

3. (c)

   the parameters θ and η are equal to the following:

   • $\theta =\mathrm{2ln}\mu -\frac{1}{2}\ln \omega$

   • $\eta =\sqrt{\ln \omega -\mathrm{2ln}\mu }$

Notwithstanding paragraph 5, where non-proportional reinsurance covers homogeneous risk-groups within a segment, the estimated adjustment factor for non-proportional reinsurance shall be equal to the following:

• $\mathrm{NP\prime }=\frac{\sum _h{V}_{\left(\mathrm{prem,h}\right)}\times {\mathrm{NP\prime }}_{\left(h\right)}}{\sum _h{V}_{\left(\mathrm{prem,h}\right)}}$

where:

1. (a)

   V _{( prem,h )} denotes the volume measure for premium risk of the homogeneous risk group h determined in accordance with paragraph 3 of Article 116;

2. (b)

   NP′ _{( h )} denotes the estimated adjustment factor for non-proportional reinsurance of homogeneous risk group h determined in accordance with paragraph 5.