SOA Exam ALTAM Sample Question 12
Study guide: Exam ALTAM
Person G, who is age 45, has recently suffered a disabling injury on the job. G's prognosis is uncertain. His annual salary before the accident was 100,000
Person G receives a structured settlement from MRH Insurance. The settlement is a life annuity, starting immediately, and payable continuously at a rate of 90,000 per year while G is disabled. An additional annuity of 20,000 per year is payable continuously while G's prognosis is uncertain for up to two years, to offset medical expenses.
Part a (1 point)
State two reasons why structured settlements often use an annuity format rather than a lump sum.
Part b (1 point)
State two possible reasons why the long term annuity would replace less than 100% of G's pre-injury earnings.
Part c (2 points)
MRH uses the following multiple state model:
You are given:
(i) MRH calculates policy values equal to the expected present value of future benefits.
(ii) i = 0.04
You have calculated the following table of annuity values and transition probabilities:
x |
\bar{a}_x^{00} |
\bar{a}_x^{01} |
\bar{a}_x^{02} |
\bar{a}_x^{11} |
\bar{a}_x^{22} |
{}_2p_x^{00} |
{}_2p_x^{01} |
{}_2p_x^{02} |
|---|---|---|---|---|---|---|---|---|
| 45 | 0.559 | 5.540 | 7.161 | 19.948 | 10.703 | 0.0301 | 0.2766 | 0.6164 |
| 47 | 0.559 | 5.420 | 7.104 | 19.528 | 10.623 | 0.0301 | 0.2766 | 0.6162 |
Show that the expected present value of future benefits at t = 0, the start date for the annuity payments, is 705,700 to the nearest 100. You should calculate the value to the nearest 1.
Part d (4 points)
(i) Show that {}_2V^{(0)}, the policy value at t = 2 if G is in State 0 at that time, is 689,700 to the nearest 100. You should calculate the value to the nearest 1.
(ii) Calculate {}_2V^{(2)}, the policy value at t = 2 if G is in State 2 at that time.
(iii) Show that the expected present value at t = 0 of the policy value at t = 2 is 564,000 to the nearest 1,000. You should calculate the value to the nearest 10.
(iv) Calculate the expected present value at t = 0 of the payments during the first two years.
Part e (2 points)
The chief actuary of MRH reviews your assumptions. The chief actuary asks you to redo your calculations, increasing \mu_{45+t}^{01} by 0.01 for all t, with no other changes.
(i) State with reasons whether the value of {}_2V^{(2)} will increase, decrease, or stay the same as a result of this change.
(ii) State with reasons whether the expected present value, at age 45, of the policy value at the end of two years will increase, decrease or stay the same as a result of this change.
(LTAM, Spring 2019, Question 2)
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