SOA Exam ALTAM Sample Question 20
Study guide: Exam ALTAM
An insurer uses the following model for joint life policies.
You are given the following additional information
(i) \mu_w^* is the force of mortality for a life age w under the Standard Ultimate Life Table.
(ii) \mu_{x+t:y+t}^{01} = \mu_{y+t}^* - 0.0005; \mu_{x+t:y+t}^{02} = \mu_{x+t}^* - 0.0005; \mu_{x+t:y+t}^{04} = 0.0005
(iii) \mu_{x+t:y+t}^{13} = 1.2\mu_{x+t}^*; \mu_{x+t:y+t}^{23} = 1.05\mu_{y+t}^*
(iv) i = 0.05
(v) For x = 40 and y = 50, \bar{a}_{x:y:\overline{10}|}^{00} = 7.8487 and \bar{A}_{x:y:\overline{10}|}^{03} = 0.00789
Part a (2 points)
Describe two ways that dependency is incorporated in this model.
Part b (3 points)
(i) Calculate {}_{10}p_{50}^{23}.
(ii) Calculate {}_{10}p_{x:y}^{00} for x = 40 and y = 50.
Part c (3 points)
A couple, (x) who is age 40 and (y) who is age 50, buys a special 10-year joint life insurance policy with the following features:
- Level premiums are payable continuously while in State 0.
- A death benefit of 100,000 is payable immediately on the second death.
- If the deaths are simultaneous, the death benefit is increased to 300,000.
Calculate the annual net premium rate.
Part d (2 points)
State with reasons whether each of the following would be higher, lower or stay the same if \mu_{x+t:y+t}^{23} is increased to 1.15\mu_{y+t}^*, assuming all other transition intensities are as given above.
(i) \bar{a}_{x:y:\overline{10}|}^{00}
(ii) \bar{A}_{x:y:\overline{10}|}^{03}
(iii) \bar{a}_{x|y}
(iv) The annual net premium for the contract in (c).
(This is Question 3 from the Fall 2019 Written Answer exam.)
Answer this question and see the worked solution