Actuarial or Linear Risk

To convert the words of the second definition of risk into mathematics, let chance be probability, loss be consequences, and 

A useful example of equation 1.4-1 is insurance, which was invented by the 15th century Genoese to protect against individual N R-n C (14-2) 

The insurance company receives N R in premiums it pays out n C and breaks even (neglecting insurance company expenses) when these are equal (equation 1.4-2). Solving equation 1.4-2 for risk gives equation 1.4-3. As N becomes very large, the ratio, n/N, approaches probability, p (Section 2.3). Thus, R = p C, as stated in equation 1.4-1, 

To illustrate, if you are in an age group with 1% probability of dying per year and the insurance pays 10,000, your annual premium must be at least 100 for the insurance company to break-even without considering the insurance company s expenses. 

A risk equation for nuclear power may be derived by imagining a world with a very large nuclear power plant population. All plants are identical with the same demography and meteorology. The plants are separated such that one does not affect the other. Each year, n, plants fail in the ith failure mode, causing a population dose tf,. If the effects are additive, the population dose (other risk measures could be used) is linearly proportional to the number failing (Equation 1.4-4), where ( is 

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