SOA Exam ALTAM Spring 2026, Question 2
Study guide: Exam ALTAM
An insurer offers a fully discrete two-year special joint life insurance policy to a couple aged x and y. You are given the following policy information:
(i) A death benefit of 10,000 is payable at the end of the year of the first death if it occurs within two years.
(ii) A survival benefit of 500 is payable at the end of year 2 if both lives survive.
(iii) A 50% refund of the first premium without interest is payable at the end of year 1 if the policy is surrendered at that time.
(iv) The policy terminates upon the earliest of the first death, surrender, or maturity.
(v) The gross annual premium is G.
The assumptions used for profit testing this policy are:
(i) The pre-contract expense is 100.
(ii) Maintenance expenses of 50 are incurred at the start of each year.
(iii) The commissions are 5% of the gross premium in each year.
(iv) The earned interest rate is 3%.
(v) The hurdle rate is 10%.
(vi) The future lifetimes of (x) and (y) are independent.
(vii) The mortality rates are:
q_x = 0.02 \qquad q_{x+1} = 0.03 \qquad q_y = 0.04 \qquad q_{y+1} = 0.05
(viii) 10% of the policies in force at the end of the first year surrender.
(ix) The insurer does not hold reserves for this policy.
Part a (2.5 points)
(i) Determine \Pr_0.
(ii) You are given that \Pr_1 = 400. Show that G = 1100 to the nearest 100. You should calculate the value to the nearest 0.1.
(iii) Show that \Pr_2 = -200 to the nearest 10. You should calculate the value to the nearest 0.1.
Part b (2.5 points)
(i) Determine the profit signature, \Pi.
(ii) Calculate the Net Present Value.
(iii) Calculate the profit margin to the nearest 0.0001.
Part c (3 points)
(i) Explain why the insurer would be concerned about the negative emerging profit at time 2.
(ii) The insurer decides to hold a reserve at time 1, denoted {}_1V such that \Pr_2 = 0. Calculate {}_1V.
(iii) Calculate the revised Net Present Value.
(iv) Explain why the Net Present Value has decreased.
Part d (2 points)
(i) Describe two factors that insured couples should take into consideration in deciding whether or not to surrender their policy at the end of the first year.
(ii) Explain how adverse selection might impact the insurer's assumption about mortality in the second year.
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