Читать книгу Pricing Insurance Risk - Stephen J. Mildenhall - Страница 48

Lee diagrams are introduced in Lee (1988), a famous actuarial science paper. Lee diagrams are a constructive visualization of several important actuarial concepts, and we use them extensively.

Figure 3.2 reproduces the original Lee diagram. It shows claims sorted by ascending size along the horizontal axis and outcome amount on the vertical axis.

Figure 3.2 The original Lee diagram. Source: Lee (1988). Reproduced with permission of the Casualty Actuarial Society.

A Lee diagram plots outcome x on the vertical axis and probability of nonexceedance p=F(x) on the horizontal (label) axis. It is a plot of the dual implicit representation because it labels an event by F(x). The probability F(x) is equivalent to the event rank, between 0 (smallest) and 1 (largest). The Lee diagram can be obtained from the distribution function by reflecting its graph in a 45 degree line through the origin, or (more simply) from the survival function by rotating its graph by 90 degrees counterclockwise about the origin. After rotating, the horizontal axis shows the exceedance probability in reverse order, which is the same as the nonexceedance probability. Figure 3.3 panel (c) shows another Lee diagram.

Figure 3.3 Different ways of computing expected losses for a sample discrete distribution. Each event is equally likely.