SOA Exam ALTAM Fall 2024, Question 2
Study guide: Exam ALTAM
A life age 60 purchases a 5-year critical illness policy which pays 100,000 at the end of the year of death or of diagnosis of a critical illness, whichever occurs first. There is no benefit on lapse.
The insurer uses the following multiple decrement table, where decrement (1) represents deaths, decrement (2) represents critical illness (CI) diagnoses, and decrement (3) represents lapses.
x |
l_x^{(\tau)} |
d_x^{(1)} |
d_x^{(2)} |
d_x^{(3)} |
|---|---|---|---|---|
| 60 | 10,000 | 50 | 105 | 400 |
| 61 | 9,445 | 52 | 115 | 500 |
| 62 | 8,778 | 53 | 125 | 600 |
| 63 | 8,000 | 54 | 140 | 500 |
| 64 | 7,306 | 55 | 152 | 0 |
Part a (2 points)
(i) Calculate the probability that the policy generates a claim.
(ii) Given that the policy generates a claim, calculate the probability that the triggering event was a CI diagnosis.
Part b (3 points)
Assume that the respective forces of decrement for deaths and critical illness diagnoses are constant within each year of age, and assume that all lapses occur at the year end.
(i) Show that the independent rate of decrement for lapses at age 60 is 0.041 to the nearest 0.001. You should calculate the value to the nearest 0.0001.
(ii) Calculate the independent rate of decrement for deaths at age 60.
(iii) Calculate the independent rate of decrement for CI diagnoses at age 60.
Part c (3 points)
The insurer decides to restrict the definition of critical illnesses covered by the policy for new policyholders, such that the new independent rates of decrement for CI diagnoses will be 50% of the current rates. At the same time, the insurer reduces the independent lapse rate assumption to 60% of current rates. Assume that the independent mortality rates are not affected. All other assumptions are as in (b).
(i) Calculate the revised value of d_{60}^{(3)}.
(ii) Explain in words why the revised value of d_{60}^{(1)} will be greater than the original value.
Answer this question and see the worked solution