Multiple life models are useful in multiple life insurance and multiple life annuities when the payment times of benefits in these insurance products are contingent on the future life times of at least two people. A reverse mortgage is an annuity whose monthly payments terminate at the death time of the last survivor; however, actuaries have used female life table to calculate monthly payments of a reverse mortgage. This approach may overestimate monthly payments. This paper suggests a last-survivor life table rather than a female life table to avoid the overestimation of monthly payments. Next, this paper derives the distribution of the future life time of last survivor, and calculates the expected life times of male, female and last survivor. This paper calculates principal limits and monthly payments in cases of male life table, female life table and last-survivor life table, respectively. Some numerical examples are discussed.
Objectives: People are living longer, but often with diseases or chronic conditions. As a consequence, interest in resolving insurance blind spots is growing. This study provides substandard risk-relevant statistics to help substandard risks who are likely to fall in insurance blind spots obtain insurance coverage, such as the reimbursement of medical costs, as well as to stimulate insurance product development. Methods: This study uses National Health Insurance Service (NHIS) cohort data to determine the relevant statistics. The incidence rates of severe diseases are derived and compared against standard risks to establish a set of relative risk factors. These incidence rates of standard and substandard risks are then compared. Results: Currently, an individual's cancer history is used in the underwriting process for simplified issue insurance. However, underwriting focusing on hospitalization and procedures related to serious illnesses could lower premiums for substandard risks. Moreover, the statistical results could be used to expand the coverage of health insurance products. Conclusions: This study's relative risk factors can be used to derive simplified issue premium rates for substandard risks. They can also be used to implement discount and loading schemes for medical reimbursement insurance and help insurance companies implement proactive risk management.
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