SOA Exam ALTAM Sample Question 8
Study guide: Exam ALTAM
You are using the following 3-state Markov model to price a 10-year disability insurance product.
Part a (2 points)
Show that for this model, \displaystyle\sum_{j=0}^{2} \bar{a}_{x:\overline{10}|}^{0j} = \bar{a}_{\overline{10}|}.
Part b (2 points)
The product has the following features:
- The product is issued to individuals age
xwho are in the Healthy state. - The product pays a continuous disability benefit at a rate of 1000 per year while the insured is in the Temporarily Disabled state.
- The product pays a death benefit of 10,000 at the moment of death.
- Net premiums are payable continuously while the insured is in the Healthy state.
You are also given the following information:
\delta = 0.1 |
$\bar{a}_{x:\overline{10} | }^{00} = 4.49$ | $\bar{a}_{x:\overline{10} |
\mu_{x+t}^{01} = 0.04 |
\mu_{x+t}^{02} = 0.02t |
\mu_{x+t}^{10} = 0.05 |
\mu_{x+t}^{12} = 0.04t |
Show that the net premium rate for this policy is 970 per year to the nearest 10. You should calculate the rate to the nearest 1.
Part c (2 points)
Let {}_tV^{(i)} denote the net premium policy value for a policy in state i at time t. You are given:
{}_3V^{(0)} = 1304.54 \qquad {}_3V^{(1)} = 7530.09
Calculate \dfrac{d}{dt}\,{}_tV^{(0)} at t = 3.
Part d (3 points)
Your company is considering adding an additional feature to this product. Under this additional feature, the insurer would return the sum of the premiums paid at the end of 10 years without interest if no benefits were paid during the life of the policy.
Calculate the increase in the net premium rate payable continuously for the product as a result of including this feature.
(MLC, Spring 2015, Question 1)
Answer this question and see the worked solution