Читать книгу Pricing Insurance Risk - Stephen J. Mildenhall - Страница 26

In this section we introduce a Simple Discrete Example and three more realistic Case Studies. These are used throughout the book to illustrate the various methods presented in the theory chapters.

We include simple examples to familiarize practitioners with the computations required to implement the methods we cover. The Cases aim to help practitioners develop an intuition for how each method prices business, informing their selection of an appropriate method for an intended purpose without resorting to trial and error.

The Cases share several common characteristics.

 Each includes two units, one lower risk and one higher.

 Reinsurance is applied to the riskier unit.

 Total unlimited losses are calibrated to ¤ 100. (The symbol ¤ denotes a generic currency.)

 Losses are in ¤ millions, although the actual unit is irrelevant.

For each Case Study:

 Figures 2.2, 2.4, and 2.6 show densities. The horizontal axis shows loss amount. In each figure the top row shows gross losses and the bottom row shows net. The left column uses a linear scale and the right a log scale.

 Figures 2.3, 2.5, and 2.7 show bivariate plots of one unit against the other. The three plots show the gross and net logdensities, and the right plot shows a scatter plot of a sample. The two units are assumed independent. These plots show where the bivariate distribution is concentrated.

Figure 2.2 Tame Case Study, gross (top) and net (bottom) densities on a nominal (left) and log (right) scale.

Figure 2.3 Tame Case Study, bivariate densities: gross (left), net (center), and a sample from gross (right). Impact of reinsurance is clear in net plot.

Figure 2.4 Cat/Non-Cat Case Study, gross (top) and net (bottom) densities on a nominal (left) and log (right) scale.

Figure 2.5 Cat/Non-Cat Case Study, bivariate densities: gross (left), net (center), and a sample from gross (right). Impact of reinsurance is clear in net plot.

Figure 2.6 Hu/SCS Case Study, gross (top) and net (bottom) densities on a nominal (left) and log (right) scale.

Figure 2.7 Hu/SCS Case Study, bivariate densities: gross (left), net (center), and a sample from gross (right). Impact of reinsurance is clear in net plot.

We strongly recommend that the reader reproduce the Examples and Cases. We suggest a general-purpose programming language such as R or Python, although SQL or even a spreadsheet suffices, with a bit of ingenuity. See Section 2.4.5 for a discussion of the implementation we used.