Risk capital allocation and risk quantification in insurance companies
Abstract
The objective of this thesis is to investigate risk capital allocation methods in detail
for both non-life and life insurance business. In non-life insurance business loss models
are generally linear with respect to losses of business-lines. However, in life insurance
loss models are not generally a linear function of factor risks, i.e. the interest-rate
factor, mortality rate factor, etc.
In the first part of the thesis, we present the existing allocation methods and discuss
their advantages and disadvantages. In a comprehensive simulation study we examine
the allocations sensitivity to different allocation methods, different risk measures and
different risk models in a non-life insurance business. We also show the possible usage
of the Euclidean distance measure and rank correlation coefficients for the comparison
of allocation methods.
In the second part, we investigate the factor risk contribution theory and examine
its application under a life annuity business. We provide two approximations that
enable us to apply risk capital allocation methods directly to annuity values in order
to measure factor risk contributions. We examine factor risk contributions for annuities
with different terms to maturity and the annuities payable at different times in
future. We also analyse the factor risk contributions under the extreme scenarios for
the factor risks.