Abstract
Whereas Chaps. 3 and 4 revolved around demand for insurance, the focus of Chaps. 5 and 6 is on the insurance company (IC). Up to this point, the IC has been depicted as passive, its activity limited to charging a (fair) premium. However, an IC pursues objectives and has a host of instruments at its disposal for reaching them. The set of these instruments will be called insurance technology; it ranges from the design of products (for instance, exclusion of certain risks, “small print” in the contract) to providing services (advice regarding prevention, consumer accommodation, the settlement of claims) and on to the purchase of reinsurance and choice of strategy for capital investment.
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Notes
- 1.
Planned changes in response to the 2007–2009 financial crisis are discussed in Sect. 8.4.
- 2.
In the case of the expense ratio, evaluation at the means of the sample can be problematic in case there are scale effects (see Sect. 6.4). In that event, profitability { PROF} changes systematically with the size of the IC (indicated by premium volume { PV}). The same is true of the expense ratio { EXP} because it contains { PV} in the denominator as well. For this reason, estimated elasticities quite likely change with increasing { PV}.
- 3.
- 4.
For simplicity, the same symbol L is used for payment of losses and liabilities more generally.
- 5.
This conclusion holds only as long as variance is used as a measure of risk. For all its advantages for the primary insurer, aggregate-excess contracts are not very common.
- 6.
Quite generally, the values of the options held by shareholders and the government move in parallel. However, the effect of the exogenous changes is smaller on the government’s option, with the exception of a change in θ (see H4). Therefore, it suffices to examine the gross value of the option.
- 7.
The average value of the correlations amounts to 0.11, pointing to a preponderance of positive correlations. This contradicts the theoretical development that is based on σ pL ≤ 0 [see explanation of hypothesis H2 and equation (5.22)].
- 8.
This index of concentration is given by { HERF} = ∑m i 2, with m i : = share of the i-th line of business in total premiums written. In the case of a uniform distribution over the n lines, one has { HERF} = ∑(1 ∕ n 2) = m(1 ∕ n 2) = 1 ∕ n.
- 9.
The exposition follows Ezra (1991). Therefore, L t does not represent current loss payments but total liabilities in the sense of present value of future payments.
- 10.
Actually, the authors posit a risk utility function with constant relative risk aversion having slightly different properties than (5.37).
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© 2012 Springer-Verlag Berlin Heidelberg
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Zweifel, P., Eisen, R. (2012). The Insurance Company and Its Insurance Technology. In: Insurance Economics. Springer Texts in Business and Economics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20548-4_5
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DOI: https://doi.org/10.1007/978-3-642-20548-4_5
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