SOA Exam ALTAM Sample Question 5
Study guide: Exam ALTAM
You are analyzing costs associated with a medical condition. You model the progression of the condition after a new diagnosis using the following 4-state model.
You are given the following information. Time t is measured in years from the date of diagnosis.
(i) \mu_t^{01} = a + be^{ct} where a = 0.4, b = 2.0, and c = 0.7;
(ii) \mu_t^{12} = 0.2; \quad \mu_t^{21} = 0.4; \quad \mu_t^{13} = 0.1
(iii) \delta = 0.04
(iv) \bar{a}_0^{01} = 2.930; \quad \bar{A}_0^{01} = 1.5185
Part a (3 points)
(i) Show that, in this case, \dfrac{\bar{A}_0^{03}}{\bar{a}_0^{01}} = \mu_0^{13}.
(ii) Calculate the value of \bar{a}_t^{\overline{11}}.
(iii) State with reasons whether \bar{a}_t^{\overline{11}} is bigger, smaller or the same as \bar{a}_t^{11}.
Part b (4 points)
The cost of nursing care in State 1 is 12,000 per year, incurred continuously. The cost of surgery is 22,000. There are no nursing care costs in State 0 or State 2.
(i) Calculate the expected present value of the cost of surgery for a newly diagnosed patient.
(ii) Calculate the expected present value of the nursing care costs for a newly diagnosed patient.
(iii) COVID-19 precautions result in additional costs at a rate of 8,000 per year for the first 4 months of each period in State 1.
Write down an integral expression for the additional expected present value, using continuous sojourn annuities.
Part c (2 points)
As a result of reorganization, the value of \mu_t^{13} is increased to 0.2. All other transition intensities stay the same.
(i) State with reasons whether the expected present value of the cost of nursing care will increase, decrease, or stay the same.
(ii) State with reasons whether the expected present value of the cost of surgery will increase, decrease, or stay the same.
(LTAM, Fall 2021 Form A, Question 3)
Answer this question and see the worked solution