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ETC3530/ETC5353 Life Insurance Mathematics Assignment 2022
发布时间：2022-10-03
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ETC3530/ETC5353
Life Insurance Mathematics
Assignment
2022
Insurance Pricing Tool
1 Objective
An insurer sells a wide range of life insurance products. It wants to provide its front office with a pricing tool for sales. The current actuarial team has developed a pricing tool but the front office is not entirely satisfied with it. The pricing tool is available on the link below:
The actuarial team has used R software to design this preliminary version of the pricing tool, with the package shiny for the development and the package rsconnect for the deployment. Currently, this preliminary version does not include all the products the insurer sells. Using similar software, the front office has requested a more comprehensive version, with a more user-friendly platform. Further, the actuarial team used AM92 Ultimate mortality for all products in the above link, but it is not the correct mortality table for policyholders in the insurer’s portfolio.
The insurer contacted several consultants to improve the pricing tool, and you are one of them. Your task is to develop a better version of this tool, which must display (i) the graphical evolution of the premium as a function of the interest rate (minimum of 0% p .a. and maximum of 15% p .a.), and (ii) the numerical value of the premium for an interest rate selected by the user. The output is similar to what the actuarial team has already done. Users of the pricing tool should be able to select all variables described in this document. Note that the insurer sells policies to individuals
aged between 20 and 90 only.
The insurer targets two groups of policyholders whose remaining lifetimes are independent. The
mortality of the first group (y) is such that l北 = l北(A)
92 for y = 20, 21, ..., and the mortality of the second group (A) is such that ly = l
92 for A = 20, 21, ..., where lAM92 refers to the number of survivors from the AM92 Ultimate table. For instance, the number of survivors for group (y) at age 20 (i.e. l北=20) is equal to the number of survivors at age 20 + 1 = 21 from the AM92 Ultimate table. Analogously, the number of survivors for group (A) at age 20 (i.e. ly=20) is equal to the number of survivors at age 20 − 3 = 17 from the AM92 Ultimate table.
2 Task
Minimum features:
The pricing tool that you propose must contain at least the following features for the first group of policyholders (i.e. (y)):
● Single premium, or level annual premiums paid throughout the term,
● The policyholder can choose among a pure endowment, a term assurance or an endowment assurance,
● The sum assured, which could be payable either at the end of the year of death or immediately on death depending on what the user selects.
It should also be possible to select the term of the contract and the sum assured.
Expenses:
One of the requested improvements of the tool given in the template consists in including the expenses. The company wants the expenses to be set as follows:
● Initial expenses in percentage of the gross premium, applicable for both single and level premiums,
● Premium expenses (excluding the first year) in percentage of the gross premium, and incurred yearly as long as the premium is paid,
● Claim expenses in percentage of the benefit amount.
There are no premium expenses when the premium is single.
Extension to policyholders (A):
The company wishes to make all the above features available for both groups of policyholders. The tool should allow the user to choose whether the policyholder belongs to group (y) or to group (A).
Featured product:
The insurance company wants to include a newly launched product targeting couples1. All couples purchasing a contract from this company are such that the mortality from the first follows that of group (y), and the mortality of the second follows that of group (A). You can find a description of your featured product using your Student ID on the following link:
3 Instructions
● This is an individual assignment,
● R packages can be used.
● Submit a PDF file containing:
(a) your name and student number,
(b) a short text (NO MORE THAN 200 WORDS) describing the features of the pricing tool,
(c) the link to the shiny pricing tool, and display the name of your featured product,
(d) the answers to the questions in the file of the featured product, and display the name of your featured product.
● Separately, submit the R script containing the code used for designing the tool, in a ‘.R’ format, not ‘.rmd’ or any other format.
● There is a significant number of students in this unit. Thus, providing the grades may take some time. Please help the teaching team by submitting your work according to these instructions.
● Consultation times will be scheduled to provide support in R. Note that it is usually hard for the teaching team to provide help when you send an R code by email, because it is necessary to have some context and to test the code in order to identify potential issues. Thus, for a more efficient feedback, it is strongly recommended to attend consultations.
4 Useful resources
The following information is also available on Moodle:
● AM92 Ultimate copy-pasted in an R script.
● shiny tutorial from an external source.
● PDF file on how to start using shiny from an external source.
● R coding resources for Life Insurance Mathematics, including a video on using R for annuities and assurances and the associated ‘.R’ file.
5 Suggested timeline
It is strongly recommended to read through the assignment and to set smaller and specific targets with deadlines. Do not leave everything to the last week before submission.
One suggestion is the following:
Step 1: Review the material on how to use R. The time this could take depends on your past experi-
ence.
Step 2: Write functions for the EPV of life annuities on (y); link them to assurances on (y) using the
premium conversion; study these EPV’s as a function of interest rate.
Step 3: Extend Step 2 to temporary products.
Step 4: Using your EPV of annuities and assurances, build functions of premiums for different prod- ucts or the minimum features.
Step 5: Review the material on how to build a shiny app.
Step 6: Build your shiny app block-by-block. For instance, start with the premium of an assurance
only for policyholders aged 25 but the interest rate can be selected. Then include age as an input variable. Then include the figure of the premium as a function of interest rate. Then
add the term. And so on.
Step 7: Include policyholders (A).
Step 8: Include expenses.
Step 9: Answer the questions of your featured product and derive the EPV of that product. Step 10: Include the featured products to your shiny app.
6 Grading
● The details regarding the assessment of the tool are given in the table below. For each product, the full mark is given when both the premium and its evolution in function of the interest rate are correctly calculated.
● Originality is taken into account for up to 10 points, with 0/10 if the layout of your tool is similar to that of the template. Think of this tool as being presented to the manager of the marketing team, or to a client, so make it user-friendly. Some desirable features include hiding input variables which are not necessary for a given product (e.g. once you choose a
single life annuity, all inputs related to assurances and joint life products would disappear).
● The questions in the PDF file are graded on 10, which is equally spread across the number of questions. If the EPV of the featured product is incorrect, it is reasonable to assume that the numerical value on the shiny app will also be incorrect.
● The maximum number of points is 100.
● Penalties: up to 10 points for not submitting the work in the requested format, and 2.5 points per-day for late submissions. You must use the featured product associated to your student number.
|
Features |
Marks |
|
Minimum features |
20 |
|
Including (A) to the basic template |
10 |
|
Including Expenses to the basic template |
10 |
|
Featured product on shiny without expenses |
35 |
|
Expenses for the featured product |
15 |
|
Questions on the featured product |
10 |
|
10 points for the originality (assignment total capped at 100) |
|
