Premiums and Reserves in Multiple Decrement Model

A guiding principle in the determination of premiums for a variety of life insurance products is $$\mbox{Expected present value of inflow} = \mbox{Expected present value of outflow}. $$ Chapter 2 discusses how the multiple decrement model studied in Chap. 1 is useful to find the actuarial present value of benefit when it depends on the mode of decrement. It aims at finding the actuarial present value of the benefits in multiple decrement models when the benefit is payable either at the moment of death or at the end of year of death. Actuarial present value of the inflow to the insurance company, via premiums, does not depend on the mode of decrement. Hence, this part of the premium computations remains the same as for the single decrement model. When the two components of premiums are determined, premiums are calculated using equivalence principle. Section 2.3 discusses the premium computations. In many life insurance products there is a provision of riders. For example, in whole life insurance the base policy specifies the benefit to be payable at the moment of death or at the end of the year of death. Extra benefit will be payable if the death is due to a specific cause, such as an accident. Premium is then specified in two parts, one corresponding to the base policy and the extra premium corresponding to extra benefit. Computations of premiums in the presence of rider is also illustrated. Another important actuarial calculation is the reserve, that is, valuation of insurance product at certain time points when the policy is in force. Section 2.4 illustrates the computation of reserve in the setup of multiple decrements. R commands are given for all these computations.