ACTL5105代做、代写Python/Java程序设计

日期：2024-04-06 12:26

THE UNIVERSITY OF NEW SOUTH WALES

SCHOOL OF RISK AND ACTUARIAL STUDIES

TERM 1 2024

ACTL5105

Assignment

Due: Sunday 15 April 2024 5pm

This is an individual assignment. The total mark is 100 and is 20% of total

course mark.

Assignment Tasks

As a life actuary you are tasked with the following two tasks.

Task I (25 marks)

Create life tables that list the values for Ax, ¨ax,

2Ax, (IA)x, and (Ia¨)x assuming an

annual interest rate of 5% for the population in the excel file “A-population-2020”.

(Instructions: You’ll need to use software, like Excel, for the calculations. However, you’re not limited to any specific software choice.)

Please arrange the values into columns, following the same order and structure as

AM92 in the Formulae book (pages 96-98). Please provide only the final numerical

values here, without including the calculation process and Excel spreadsheets in the

main document. If you choose to include calculation methods and Excel spreadsheets, add them to an appendix, which won’t be evaluated. There are no specific

guidelines for the appendix.

Page limit: 4 A4 pages maximum.

Task II (75 marks)

Consider unit-linked endowment policies that offer a guaranteed minimum death

benefit with the following key features:

? The policies has a term of 30 years.

? There is a guaranteed minimum death benefit of $100, 000.

? On death of the policyholder, there is a benefit payable at the end of the policy

year of death of the basic sum insured or the bid value of the units allocated

to the policy, whichever is greater.

? The policyholder may surrender the policy only at the end of a policy year.

The surrender benefit is the same as the bid value of the units.

1

? Level annual premiums are payable in advance until maturity or earlier death,

and 85% of each year’s premium is invested in units at the offer price.

? The units are subject to a bid-offer spread of 5%.

? The units are subject to an annual management charge of $30 plus 1% of the

bid value of the units. The management charge will be deducted at the end

of each policy year and before the death and surrender benefits are paid.

There are four options for the maturity benefit:

? Policy A: At maturity, 100% of the full bid value of the units is payable to the

policyholder if the policyholder is still alive.

? Policy B: At maturity, 105% of the full bid value of the units is payable to the

policyholder if the policyholder is still alive.

? Policy C: At maturity, 110% of the full bid value of the units is payable to the

policyholder if the policyholder is still alive.

? Policy D: At maturity, 120% of the full bid value of the units is payable to the

policyholder if the policyholder is still alive.

Calculate the premiums for the mentioned policies for a 30-year-old, based on

the following information:

? Initial Expenses: $300;

? Renewal Expenses: $100 at the start of each year starting from the second

year;

? Initial Commission: 20% of the first premium at the start of the first year;

? Renewal Commission: 2% of the premium at the start of each year starting

from the second year; No-renewal commission will be incurred to the company

during the years of suspension.

? Risk discount rate: 8% per annum;

? The company holds unit provisions/reserves equal to the full bid value of the

units. It sets up non-unit provisions (reserves) to zeroise any negative non-unit

fund cashflows.

? The company is targeting a profit margin of 12%.

2

To determine the premiums, you further make the following assumptions on the

following variables: morality, rate of surrender, unit fund growth rate, and non-unit

fund interest rate.

Assumptions

? Mortality: “A-population-2020” (posted on the course website);

? Independent rate of surrender: 5% pa for the standard policy;

? Unit fund growth rate: 7% per annum;

? Non-unit fund interest rate: 3% per annum;

? Since surrender is only allowed to happen at the end of the year, it is generally not worthwhile for a policyholder to surrender in the final year. So you

assumes that there are no surrenders in the last year of the term (that is, the

independent rate of surrender in final year is 0).

(i) Provide the final numerical results for the annual premiums for the above policies. The premiums should be rounded to the nearest integer.

(Instructions: You’ll need to use software, like Excel, for the calculations. However, you’re not limited to any specific software choice.)

Page limit: 1/2 A4 pages maximum.

Font size: greater than Time New Roman font 12pt.

(ii) Outline the algorithm of your calculation in (a).

(This part is for the marker to decide whether the procedure you used in determining the premiums is reasonable. You should include all the steps involved in

your calculation while describing the algorithm, but try to avoid paragraphs and

long sentences. Use bullet points and/or numbers to list the steps. You can use the

standard notations used in lecture notes and formulas. )

Page limit: 2 A4 pages maximum.

Font size: greater than Time New Roman font 12pt.

(iii) Given the volatile economic environment where investment growth rates can

vary significantly, analyze the sensitivity of the profit margin to changes in the

unit fund’s growth rate. You should recalculate the profit margin for each policy,

using the (integer) premium initially determined in (i) and adjusting the unit fund’s

growth rate by +1% and ?1%, and then by +2% and ?2%, while maintaining all

other factors constant, and provide a brief discussion of the outcomes.

Only the numerical results for the profit margin adjustments and a discussion

should be provided here. Detailed calculations and methodologies should not be

included here.

Submission

3

? The font size of the main body of your assignment must be at least 12pt.

? The assignment you submit must have a title, your name and zID.

? Assignments must be submitted via the Turnitin Submission Inbox that is

available on the course website (in the Assignment section). As long as the

due date has not been reached, you can resubmit your work: the previous

version of your assignment will be replaced by the new version.

? All parts of your assignment must be uploaded as a unique pdf document.

? Please check Course Outlines for the School policy on late assignments.

? Students are reminded of the risk that technical issues may delay or even

prevent their submission (such as internet connection and/or computer breakdowns). Students should then allow enough time (at least 24 hours is recommended) between their submission and the due time. The Turnitin module

will not let you submit a late report. No paper copy will be either accepted

or graded.

? Programming code or spreadsheets should not appear in the main body. They

must be provided as appendices at the end of your assignment.

? The font size requirement does not apply to the appendices.

4