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Reserve Recursion Formula

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  • Reserve Recursion Formula

    Hello,

    I'm working through the ASM manual portion on the recursive reserve formula. I've encountered a problem (37.2) involving a deferred life annuity due. Why is the death benefit in the formula set to zero?

    thanks

  • #2
    Can you post the question for those who don't have the manual? Thanks.
    act justly. walk humbly. .

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    • #3
      I'm guessing because its an annuity, not life insurance. A standard annuity doesnt pay a death benefit.

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      • #4
        If you're still in the time of deferment where you aren't getting any annuity payments, the expected amount the insurer pays that year has to be zero. If you're at the part where you're receiving the annuity, the payments the annuitant makes will be zero.
        Whether you are the lion or the gazelle, when the sun comes up, you better be running.

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        • #5
          Here's the problem.

          For a fully discrete 10-year deferred life annuity-due on (50), premiums are payable at the beginning of the year for the next 10 years. Premiums are based on the equivalence principle. You are given:

          (i) a double dot 50:10 =6.9
          (ii) a double dot 50 = 11.3
          (iii) 10_E_x = 0.44
          (iv) q_59 = 0.012
          (v) i = 0.06

          Calculate 9_V.

          Is Philly's explanation that this is an annuity and not an insurance with death benefits the best for why b_10 = 0?

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          • #6
            I'm pretty sure my explanation is the best.
            Whether you are the lion or the gazelle, when the sun comes up, you better be running.

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            • #7
              Looking at the problem, Ken's explanation seems to be correct.

              As a follow up, if this wasn't in the deferral period, would you replace the DB_t*q_x+t-1 in the recursion formula with (benefit payout)*p_x+t-1?

              thanks

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              • #8
                That sounds right. Also, your payment will be zero.
                Whether you are the lion or the gazelle, when the sun comes up, you better be running.

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