Risk capital allocation and risk quantification in insurance companies

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.