这是一个荷兰的精算**R语言代写**作业

Introduction

In France, the viager system is a special type of home sale. Under this type of agree

ment, the buyer agrees to pay the seller a down-payment and/or a whole life annuity in

exchange of the house ownership. Normally, the sellers will be allowed to stay in the sold

property for the rest of their lives. This essentially makes the price of the property a life

contingency.

This contract is attractive to the house owners, normally retired people because it allows

them to extract values from their asset without making them homeless. For the buyers,

these type of properties are normally priced lower than the market price. Moreover, they

can gamble on the life of owners. If the owner passes away shortly after the sale, the

buyer would have acquire a house with low price. However, the whole life annuity in this

contract has to be payed until the seller pass away even if they out live the buyer. So it

would be unfortunate if the buyer buys the house from Jeanne Calment (Google it).

In this assignment, your group is required to design a simple viager sell and help to set

the payment level.

1 Setting

You are tasked to calculate the payment level for the whole life annuity for a specific

viager house sale and also assess the variance of the whole life annuity’s present value.

The default setting is as follows:

(a) This sale takes place in a city/town of your choice, so not necessarily France. Please

name the place in the first page of your report.

(b) The sale is solely paid for by a whole life annuity, so no down-payment. The specific

of the annuity will be given later but the actuarial present value of the annuity should

be equal to 80% of the market value of a typical apartment/house at the sale location.

(c) To keep the question simple, the effective annual interest rate used for discounting

is assume to be a constant and positive through the whole contract. You may pick

this interest rate yourself but you have to provide support/reasoning.

(d) Use the uniform distribution of deaths assumption for fractional age.

(e) In order to diversify the assignments, the problem settings will be personalized.

Details will be given later in this document.

2 Mortality Models

Use the national life table for the location of your choice in the calculation and provide

proper reference. You are expected to adjust your calculation based on the condition of

the owner for the house. There are three possible owners.

(1) A 50 years old female smoker. It is assumed that the probability of dying in the

following year for all ages (qx; 8x) would be 1.4 times higher than national average.

Hint: Remember to adjust the probability at the limiting age such that the life table

remains a valid probability model.

(2) A 62 years old man who recently has surgery. After assessing the risk involved, the

selected probability of survival after having such a surgery are:

p[62] = 0:7; p[62]+1 = 0:8; p[62]+2 = 0:82; p[62]+3 = 0:85:

and the selection period is 4 years.

(3) The owners are a heterosexual couple, both at 60 years old. The whole life annuity

needs to be paid until both owners have passed away. For simplicity, you may

assume that the mortality of the partners is independent of each others.

3 Payment timing and frequency

All whole life annuity is annuity-due and all payment has the same face value. The pay

ment frequency has the following 4 options:

(1) Half-yearly;

(2) Every 4 months;

(3) At the first month and the ninth month after closing the deal, repeating the same

pattern every year afterward;

(4) Monthly.

4 Personalized assignment: explanation

By enrolling as a group on Nestor, you will get a group number. A code is associated to

each group number. This code uniquely determines your group assignment. For instance,

if you get 1-1, this means you have to finish the assignment assuming the house owner

is a 50 years old smoker with the payment-due every 6 months. For an overview of the

group numbers and the codes, a coresponding table will be uploaded to Nestor after the

grouping is finished. It is crucial that you do the assignment corresponding to your group

number. We will only grade your assignment if you have made the right one. So double

check your code and make sure that you make the right assignment.

5 Assignment tasks

Here we formulate the assignment tasks in detail:

• Tasks to perform: Explain the exact setting and parameters you used and justify

them. Determine payment according to your assigned questioned and the general

setting. Calculate the variance of the annuity. List out all the formula you have used

in your calculation. Give your recommendation to a couple of both 30 years old if

they should buy the house with your scheme.

• Bonus task: Based on your results or otherwise, should governments encourage

using the viager system as part of the retirement support, justify your answer. Rea

sonable attempt would result in a 0.2 extra to your assignment grade, a well argued

and supported answer would add 0.5 to the final grade.

Points of attention:

− As mentioned above, you have to choose appropriate values of yourself to finish

the assignment. Do this in such a way that all calculation can be performed and

justified.

− If you feel that additional assumptions have to be made, then do so and clearly

explain and motivate this in your report.

− We expect you to complete the necessary calculation in R as this is quite compli

cated to calculate by hand.