Discrete varying insurance: decreasing term uses the same summation as increasing term but with what modification?

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Multiple Choice

Discrete varying insurance: decreasing term uses the same summation as increasing term but with what modification?

The key idea is that the timing of the benefit changes between increasing and decreasing term insurance. In the discrete increasing term, the payoff at the end of year k+1 grows with time, so the amount used in the sum is k+1. For a decreasing term with the same term length, the payoff is largest at the start and declines each year, so the amount at the end of year k+1 should be n−k. Thus, to convert the summation from increasing to decreasing term, you replace the factor (k+1) with (n−k). The index runs from k = 0 to n−1, so you’d be summing terms like (n−k) times the appropriate probability and discount factor. For example, with n = 5, the increasing term uses 1, 2, 3, 4, 5; the decreasing term uses 5, 4, 3, 2, 1.

The key idea is that the timing of the benefit changes between increasing and decreasing term insurance. In the discrete increasing term, the payoff at the end of year k+1 grows with time, so the amount used in the sum is k+1. For a decreasing term with the same term length, the payoff is largest at the start and declines each year, so the amount at the end of year k+1 should be n−k.

Thus, to convert the summation from increasing to decreasing term, you replace the factor (k+1) with (n−k). The index runs from k = 0 to n−1, so you’d be summing terms like (n−k) times the appropriate probability and discount factor. For example, with n = 5, the increasing term uses 1, 2, 3, 4, 5; the decreasing term uses 5, 4, 3, 2, 1.

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