Is why we have defined it with an index n in equation

is why we have defined it with an index, n , in equation
(4). In Table 1, we give an example of the diversification
benefit as reported by SCOR during its Investor Day in
July 2009 (SCOR 2009). Even if they are a little dated,
these figures are a good illustration of the advantage
to be gained by examining the diversification benefit
obtained by a company when the calculation of its capital
is based on all the risks involved. It can be seen, for
example, that in the case of a reinsurer, investments only
represent a small portion of the risk in comparison with
the portfolio, although their individual capital corresponds
to more than half the individual capital of the company’s
life insurance business. In the end run, when its main
business lines are considered, the company achieves
a diversification benefit of 47%, which is considerable.
The figures published by other reinsurers are similar. The
diversification benefit is essential for this type of business
to operate smoothly (Boller and Dacorogna, 2004).
Reinsurers therefore take particular care when modelling
their portfolios.
To complete this brief incursion into the world of internal
models, we would like to mention that at least three types
of quantitative model exist for insurance risks:
1. Stochastic-type models based on probability
distributions and more or less sophisticated
modelling of risk interdependence. Generally
speaking, the internal models of companies
belong to this category.
2. Deterministic-type models, or factor models. The
capital is calculated by multiplying the volume
of business by a specific factor (often called the
capital intensity). These models are typically
used by rating agencies to estimate the capital
requirements of the companies they are rating.
3. Scenario-based models. Several scenarios are
applied to the economic balance sheet to
examine the value of the company in relation to
different states of the world. These models, also
called stress tests, were applied by the FED
to American banks in March 2009. The positive
results restored market confidence in the financial
system.
Table caption:
Internal Model Results for SCOR as published in 2009
Risk capital (RC) of group
(net of reinsurance)
Individual RC Diversified
RC
Total portion of
RC
Diversification
benefit
New P&C business 1200 820 24% 32%
P&C reserves 1600 1240 36% 23%
Life business 1800 900 26% 50%
Investments 970 130 4% 87%
Counterparty and credit risks 280 40 1% 86%
Risks due to exchange rate and other
positions on the economic balance sheet
330 60 2% 82%
Operational risks 210 210 6% 0%
Total 6720 3400 100% 47%
(4)

SCOR paper n°34 - A Change of Paradigm for the Insurance Industry
9
Most companies use a combination of these approaches.
While deterministic models are preferred because they
are simple to use and give almost instantaneous answers
to the questions posed, they are not very flexible. Factors
that have been determined in certain situations may be
less influential in other circumstances or if there is a
substantial change in the insurer’s portfolio. The other
two types are basically the same. Stochastic models