Hello This question relates to the South African F102 Syllabus What is the difference between the various claim inception rates including a description of when we use it rate : initial claim inception rate central claim inception rate type a central claim inception rate type b I would really appreciate any help or insight with this Thanks in advance!
Hi Jessi This is a particularly complicated part of the F102 course. To reassure any students sitting SP2, it is not part of SP2. In F102 Chapter 28 we are trying to price income protection policies. To do that we need a probability similar to the q_x we use for mortality calculations. The difficulty is in determining what age x should refer to, ie the age when someone falls ill, or the age when someone starts to receive benefits. The difference between these two ages is the deferred period, d. So we have two different rates (see page 15): Type a - here age x is the age at which the benefits start to be paid. So the policyholder actually became sick at age x-d. Type b - here age x is the age at which the policyholder fell sick. So benefits will start at age x+d. Strictly speaking these are central probabilities, so we are looking at the number of claims/sicknesses for lives aged between x and x+1 divided by the average number of lives aged between x and x+1. The type a rates are given in the Tables on page 138. The type b rates are not in the Tables. So if you are using the Tables to answer a question in the exam, it would have to be the type a rates. Consider a policyholder that takes out an IP policy at age 30 when they are healthy (this is the assumption that the Tables make). In order to make a claim or fall sick at age x, they need to have survived from age 30 to age x. Again we have two possibilities (see page 16): For initial rates we use a survival probability that requires the policyholder to be healthy at age x-d, as the initial claim inception rate is a probability for healthy lives. In contrast, for central rates we use a survival probability that requires the policyholder to be alive (either healthy or sick) at age x+0.5, as the central claim inception rate is a probability for all lives (regardless of health status). Which rates you would actually use in practice would depend on the purpose of the calculation and the type of data that you had collected. I hope this helps. Best wishes Mark
