Life Contingencies (STAT3037/6043)
Lecture Notes Week Five Further Issues in Premium
Calculations and Accumulations
Gross Premium Calculations
So far in this unit we have only calculated net premiums, that is, premiums
that only allow for the expected cos
Life Contingencies (STAT3039)
Lecture Notes Week Nine Increasing Annuities and
Applications of Reserves
Increasing Annuities
Last week we considered increasing assurance contracts. Just as the benefit
from an insurance contract can increase over time, so
Life Contingencies (STAT3039)
Lecture Solutions Topic 9
9.1
Compare the EPVs of the two annuities.
For the level annuity the EPV is:
200a 60 = 2,826.80.
For the increasing annuity, let the annual increase be h:
100a 60 + h(Ia)60
= 100a 60 + h [ (Ia)60 60
Life Contingencies (STAT3037/6043)
Lecture Solutions Week 11
11.1
(a)
The prospective policy value at the end of the first year per policy in force =
1
= 100, 000 A36:19| Pa36:19|
= 100, 000 ( A36 19 p36v19 A55 ) 146.20 ( a36 19 p36v19 a55 )
= 2062.31 197
Life Contingencies (STAT3037/6043)
Lecture Solutions Week 10
10.1
(a)
If T is the joint life status for (80) and (85) then:
P(5 < T < 10) = P(T > 5) P(T > 10)
= 5p80:85 10p80:85
= 5p80.5p85 10p80.10p85
(b)
If T is the last survivor status for (80) and (85
Life Contingencies (STAT3037/6043)
Lecture Notes Week Six Reserves and Policy Values
Reserves
A reserve is money that an insurer sets aside to meet its future payments, ie
benefits to policyholders and expenses.
In many life insurance contracts, the expec
Life Contingencies (STAT3037/6043)
Lecture Solutions Week 13
13.1
20
i)
HH HD
HI ID
5, 000 e t ( t p35 35+ t + t p35 35+t ) dt
0
15
ii)
HI
10, 000 e t ( t p35 ) dt
0
Explanation
The force of mortality is an example of a transition intensity so to quote th
Life Contingencies (STAT3037/6043)
Lecture Notes Week Twelve Unit-linked policies
Introduction
A unit-linked policy is a non-traditional policy which incorporate a transparent
investment component. They are also known as investment-linked or marketlinked
STAT3037/6043 LIFE CONTINGENCIES
TUTORIAL WEEK EIGHT SOLUTIONS
Question 1
(i) The expression for the mortality profit or loss under an insurance contract is
( qx+t nd ) .S (1 t +1Vx:n | )
where nd is the actual number of deaths in the final year of the co
STAT3037/6043 LIFE CONTINGENCIES
TUTORIAL EXERCISES WEEK NINE
Question 1
An impaired life aged 45 applies for a 20-year endowment insurance with a sum insured
of $10,000 payable at maturity or at the end of the year of earlier death. Level premiums
are pa
STAT3037/6043 LIFE CONTINGENCIES
TUTORIAL WEEK NINE SOLUTIONS
Question 1
a) First find the standard premium, P.
P = 10000
A45:20
0.46998
= 10000
= $341.06
&
a45:20
13.780
b) Now let P be the premium for the impaired life. The EPV of premiums is, where
das
Suppose the following applies:
A 40 year old buys a whole of life insurance, of sum insured $100,000 which is payable at end of year of death.
The level premium payable annually in advance for life = $927.
Expenses for the policy are $100 at the start of
Life Contingencies (STAT3037/6043)
Lecture Notes Week Eight Increasing Insurances and
With-Profits Policies
Varying Insurance
So far we have studied insurance benefits where the sum insured has been
constant throughout the term of the policy. A constant s
Life Contingencies (STAT3037/6043)
Lecture Notes Week Six Reserves and Policy Values
Reserves
A reserve is money that an insurer sets aside to meet its future payments, ie
benefits to policyholders and expenses.
In many life insurance contracts, the expec
Life Contingencies (STAT3037/6043)
Lecture Notes Week Seven Policy Values, Mortality Profit
and Extra Risk
Mortality Profit
In all of the calculations we have performed so far in this unit we have made
assumptions regarding investment earnings, expenses a
STAT3037/6043 LIFE CONTINGENCIES
TUTORIAL EXERCISES WEEK TEN
Question 1
An annual premium with-profit twenty year endowment insurance policy issued to a
life aged 40 has a basic sum insured of $10,000 payable at the end of the year of
death. Premiums are
Life Contingencies (STAT3037/6043)
Lecture Notes Week Ten Multiple Life Functions and
Insurances and Annuities Involving Two or More Lives
Introduction
In previous weeks we have focused on insurance contracts sold to a single
individual. It is possible to
Life Contingencies (STAT3037/6043)
Lecture Notes Week Eleven Cash flow models & profit
testing
Building basic cash flow models
The traditional method of premium determination involves equating the expected
present values of income and outgo. The premium i
Life Contingencies (STAT3037/6043)
Lecture Notes Week Thirteen Multiple Decrements and
Multiple State Models
Dealing with multiple decrements
For some contracts there is more than one way in which a policyholder may
exit. For example, for a life insurance
STAT3037/6043 LIFE CONTINGENCIES
TUTORIAL EXERCISES WEEK EIGHT
Question 1
(i) Show that the mortality profit arising at the end of the last year in force of an
endowment insurance contract with sum insured $1, under which premiums are payable
annually and
Q1: This is your warm up:
Calculate the value of:
A45:35 assuming 0% pa interest and:
(i) AM92 ultimate mortality
(ii) A constant mortality rate (qx) of 0.5
(iii) Zero mortality
Calculate the following, assuming AM92 ultimate mortality and 4% pa
interest:
Q1
A select life aged 45 purchases a 20 year term endowment assurance contract.
Level premiums are payable annually in advance throughout the contract. A sum
assured of $250,000 is payable on maturity, or immediately on earlier death.
Using the following
Life Contingencies (STAT3037/6043)
Lecture Notes Week Two Life Assurance Contracts
Introduction
A life insurance policy is a contract between a life insurance company and one
or more persons called the policyholders. In return for a payment of premiums, t
Life Contingencies (STAT3037/6043)
Lecture Notes Week One Mortality and Selection
Review of Survival Functions and the Life Table
Survival Models and Mortality Probabilities
The future lifetime of any given person is unknown and is commonly assumed
to be
Life Contingencies (STAT3037/6043)
Lecture Notes Week Four Evaluation of Assurances and
Annuities
Calculation of Present Values of Insurance Benefits
So far we have developed integral and summation formulae for common
insurance benefits. We have also intr
Life Contingencies (STAT3037/6043)
Lecture Notes Week Three Life Annuity Contracts
Introduction
Last week we began to look at Life Insurance contracts and we calculated the
expected present value of benefits under whole of life, term, pure endowment and
e
STAT3037/6043 LIFE CONTINGENCIES
TUTORIAL WEEK TEN SOLUTIONS
Question 1
(a)
Year
Benefit
1
10000
2
10200
3
10400
Equate the expected present value of the premiums with that of the benefits and expenses:
Pa[40]:20 = 9800 A[40]:20 + 200( IA)1
+ 4200
[40]:20