SOA Exam ALTAM Sample Question 29
Study guide: Exam ALTAM
A 5-year term life insurance policy with a partially accelerated Critical Illness (CI) rider is sold to a Healthy life age x. The policy is to be profit-tested using the multiple state model:
The policy pays 600,000 at the end of the year of CI diagnosis, if the policyholder is still alive at the end of that year; 1,000,000 at the end of the year of death, if the policyholder was in State 0 at the start of that year; and 500,000 at the end of the year of death if the policyholder was in State 1 at the start of that year.
Annual premiums of 30,000 are payable while the policyholder is in State 0.
You are given the following profit test assumptions:
(i) One-year transition probabilities at age x+k, for k=0,1,2, are:
p^{01}_{x+k} = 0.01 + 0.002k, \quad p^{02}_{x+k} = 0.008 + 0.003k, \quad p^{03}_{x+k} = 0.004, \quad p^{12}_{x+k} = 0.25
(ii) The state-dependent reserves are:
t |
2 | 3 | 4 |
|---|---|---|---|
{}_tV^{(0)} |
12,000 | 9,000 | 5,000 |
{}_tV^{(1)} |
280,000 | 210,000 | 120,000 |
(iii) Pre-contract expenses are 500.
(iv) Commissions are 5% of each premium including the first.
(v) Maintenance expenses in State 1 are 100 at the beginning of the year.
(vi) The insurer earns interest on investments of 6% per year.
(vii) The hurdle rate is 10% per year.
Part a (3 points)
Show that the emerging profit in year 3, conditional on being in State 0 at the start of the year, is 4,900 to the nearest 100. You should calculate your answer to the nearest 1.
Part b (2 points)
Show that the emerging profit in year 3, conditional on being in State 1 at the start of the year, is 14,200 to the nearest 100. You should calculate your answer to the nearest 1.
Part c (2 points)
Calculate the profit signature value for year 3, \Pi_3.
Part d (1 point)
You are given the first three values of the profit signature:
\Pi_0 = -500 \qquad \Pi_1 = -770 \qquad \Pi_2 = 3536
Calculate the partial net present value for the first 3 years, NPV(3).
(This is Question 5 from the Spring 2019 Written Answer exam.)
Answer this question and see the worked solution