An Insurance Plan to Guarantee Reverse Mortgages: Comment

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In Weinrobe's (1988) article arrangements of reverse mortgage plans (RM) are discussed and analyzed, particularly with respect to the deficit risk of the lender. This comment simplifies the situation by translating the RM concepts into traditional life insurance terms and using actuarial calculations, making the RM commercially accessible for the life insurance industry. Further, the RM possesses interest immunization properties in conjunction with a usual life insurance portfolio. In its simplest form, an RM is an annuity paid to an individual by a financial institution with the corresponding lump-sum value paid to the institution at the end of the annuity period. The lump-sum payment is secured by a mortgage on residential property owned by the insured. The reversion, in comparison to an annuity investment, applies to the date the lump-sum payment is due, at the beginning of the annuity period in the case of the annuity investment. To extend these concepts to payments depending on the annuitant's being alive, the annuity investment must be translated to an immediate life annuity, purchased by a lump-sum payment at the beginning of the life annuity. The reversion makes the lump sum payment due at the end of the life annuity peirod, i.e., death. The size of the payment for a given size of lump sum is here calculated as an expected value by (numerical) integration instead of the corresponding simulation calculation in the Weinrobe's article. The value of a single life annuity of $1 yearly, paid continuously, is