AMA533
Mini Project
Due on 23:00, Tuesday, 1 April, 2025
Project Problem:
(1) Find and download one life table (you can choose any city or country and the year of life table, and please specify the information of the life table in your project report). Suppose that the death benefit of each life insurance is 500, 000 HKD in the first 2 years of issue (no matter when is the issue age) and it is increased to 1 , 000, 000 HKD in the second 2 years and it is then reduced to 800, 000 after these 4 years from issue. The effective annual interest rate i = 0.01. Suppose that the life time distribution in your downloaded life table follows constant force of mortality within each year of age. Suppose the upper age limit is 100.
Compute both the discrete (payable at the end of the year of death) and continuous (payable at the moment of death) EPV (or equivalently, APV) of
(a) whole life insurance;
(b) 10-year term life insurance;
(c) 20-year endowment insurance with pure endowment payment of 500 , 000 HKD;
(d) 10-year deferred life insurance;
starting at ages (20) and (30) respectively for the policyholder.
(2) Use the same information and the life table in part (1). Compute the fully discrete and fully continuous premiums of
(a) whole life insurance with premiums for whole life;
(b) 10-year term insurance with premiums for 10 years;
(c) 20-year endowment insurance with pure endowment payment of 500 , 000 HKD and premiums for 10 years;
starting at ages (20) and (30) respectively for the policyholder.
(3) Use the same information and the life tables in part (1). For all insurance policies and premium types in part (2) (including both fully discrete and fully continuous premiums), com- pute the net reserves for 10 consecutive years starting from age (20) and age (30) respectively. Graph these net reserves over 10 consecutive years starting from age (20) and age (30) respec- tively as the bar-chart.
Note:
• For all computations and graphs above, please feel free to choose the use of excel (at- tach your excel tables in your report), python, Matlab, Mathematica, C++ and/or other statistics softwares such as SAS or R. Please include your downloaded life table, program- ming codes or calculation details and all computation results and graphs into your report. Each student needs to submit his/her own report to Blackboard. You need to submit the scanned copy or photo copy of your report as a single PDF file. No late report will be accepted. The report will weight 10% of your semester grade.
• Please double-check your uploaded file. Any missing results will be considered incomplete.