Mathematical Finance

UNIT VIII

Mathematics of Insurance

1. Life Annuities

2. Life Insurance

3. Property and Casualty Insurance

Unit VIII Summary

List of Formulas

Exercises for Unit VIII

1	Life Annuities

Life annuities are different from the annuities certain that we discussed earlier. In a major distinction, life annuities are more related to life insurance for being contingent. A contingent contract involves a sequence of payments that are dependent on an occurrence of a certain event that cannot be foretold. In this case, it is either death or living up to a certain age. This element of uncertainty requires the use of probability distribution, which in this context is in the form of a mortality table. Like life insurance, life annuities are dealt with by insurance companies and the person to whom the annuity would be payable, is called an annuitant, as opposed to the “insured”. Life insurance proceeds are payable to survivors upon the death of the insured.

The typical stated premium of life annuities and life insurance is usually a gross premium, which includes the loading costs in addition to the net premium. Loading costs include a company’s operating expenses and profit margin. The net premium is the pure cost of the ultimate benefits to the annuitant or the insured, usually broken down into installments unless it is paid in a single payment on the day of purchase. In this case it is called a net single premium, while a yearly installment is called a net annual premium. Our calculations ...