Half way through the solution it says "It might use risk premium or original terms reinsurance. Reserves are relatively small and so there is little difference between the two types for the purpose of transferring the morbidity risk" Reserves are relatively small because this is CI, but why does this mean there is little difference between the two types for the purpose of transferring the morbidity risk? Does the statement assume that the risk premium reinsurance would reinsure a proportion of the sum at risk rather than a proportion of the whole sum assured? I understand that in this case the sum at risk and the sum assured are (nearly) the same because reserves are small. Am I missing something here? The solution continues "But original terms also involves the sharing of lapse and expense risk, and so the company will have to decide whether it wants this (bearing in mind the cost)" Please can someone explain this? Thanks.
Risk premium reinsurance is usually based on sum-at-risk (sum assured - reserves) x morbidity rate x present value factor, whereas original terms reinsurance is based on sum assured x morbidity rate x present value factor for the morbidity risk component. Hence both should not differ by much if the reserves are small. Here I think we also need to assume that the morbidity rates used by the reinsurance company and the insurance company are the same or not differ by much in order to say such a statement. However, I'm not sure what you mean by "reserves are relatively small". Reserves are small relative to what? I can maybe guess that reserves are small relative to other products such as long-term care insurance. Then it could make sense. I agree that critical illness reserves can be small though. For original terms reinsurance, the risk-sharing aspect between the insurer and the reinsurer is embedded in the premium rate offered to the policyholder. So if increase in lapses results in premiums not being received, then the reinsurer will suffer as well. I'm not sure about expense risk though in terms of accounting, as expenses are usually deducted from net of reinsurance premiums. Perhaps it is due to the definition of original terms reinsurance being "sharing of all aspects of insurer's risk" and hence any actual expenses that are higher than expected are shared between the insurer and the reinsurer (e.g. actual minus expected expenses divided by number of polices reinsured). On the other hand, for risk premium reinsurance the reinsurer charges premiums separately to the insurer while the insurer keeps the premiums paid by the policyholder. Hence reinsurer just needs to charge a premium for the morbidity risk in relation to the proportion of insurer's business reinsured and then add a profit loading and not have to worry about insurer's other risks (e.g. lapse and expense risk) for which the loadings are made in the premiums paid from the policyholder to the insurer.
