FIN 3220A Actuarial Models I
First Term 2005-2006
Assignment 2
Hand in the solutions on or before 31 October 2005.
1.
A 2-year term insurance is issued to (30). Benefit are payable at the end of the year of death.
The death benefit for policy year t is bt
FIN 3220A Actuarial Models I
Tutorial 7
30 November 2005
1. (x) = 0.04 when x < 45, and (x) = 0.05 otherwise. Find the 75-th
percentile of the future lifetime of (25).
2. It is estimated that an impact of a medical breakthrough will be an
increase of 4 ye
FIN 3220A Actuarial Models I
Tutorial 6
23 November 2005
1. A level premium whole life insurance of 1, payable at the end of the year
of death, is issued to (x). A premium of G is due at the beginning of each
year, provided that (x) survives. You are give
FIN 3220A Actuarial Models I
Tutorial 5
9 November 2005
1. A basic life annuity due of $1 per year is paid to (90) where
x
90
91
92
93
lx
100
72
39
0
.(2)
is the survival model and i = 0.06. Find a90, assuming the UDD.
2. Let Y be the present value random
FIN 3220A Actuarial Models I
Tutorial 4
26 October 2005
1. You are given:
(i) ax = 10
(ii) 2ax = 7.375
(iii) Var(a T|) = 50
Find Ax.
2. You are given the following information for a temporary life annuity due
issued to (x):
Year t
Amount of payment
px+t
0
FIN 3220A Actuarial Models I
Tutorial 3
12 October 2005
1. You are given:
(i) i = 0.02
(ii) p50 = 0.98
(iii) A51 A50 = 0.004
(iv) 2A51 2A50 = 0.005
Let Z be the random variable representing the PV of a whole life insurance
of 1 with death benefit payable
ACTION PLAN/GANTT CHART
What it is:
An action plan/Gantt chart is a graphic representation of a projects schedule, showing the
sequence of tasks, which tasks can be performed simultaneously, and the most critical tasks to
monitor. The plan/chart can be us
Tables for
Exam M
The reading material for Exam M includes a variety of textbooks. Each
text has a set of probability distributions that are used in its readings. For those
distributions used in more than one text, the choices of parameterization may not
FIN 3220A Actuarial Models I
First Term 2005-2006
Monday 4:30pm 6:15pm, Room G04, Y.C. Liang Hall
Wednesday 9:30am 11:15am, Lecture Theatre, Basic Medical Sciences Building
Instructor: Professor Albert C.S. Wong
Office: Room 203, Leung Kau Kui Building
Ph
Introduction
In this chapter, we will determine the level of life annuity
payments necessary to buy, or fund, the benefits of an insurance
or annuity contract
By combining the ideas of APV of the payments of various
life insurance and annuities
In practic
Introduction
In this chapter, we study payments contingent on survival, as
provided by various forms of life annuities
A life annuity is a series of payments made continuously or at
equal intervals while a given life survives
It may be temporary (limited
Introduction
The models for life insurances designed to reduce the financial impact of
the random event of untimely death are developed
Life insurances are characterized by their long-term nature
The amount of investment earnings, up to the time of paymen
Introduction
The time-until-death random variable, T(x), is the basic building block in
life insurance and annuity
Another important distribution is the distribution of the age-at-death
random variable X
A life table can be used to summarize a distributio
FIN 3220A Actuarial Models I
First Term 2005-2006
Assignment 4
Hand in the solutions on or before 5 December 2005.
1.
You are given the following information:
Ax = 0.19 .
Ax = 0.064 .
d = 0.057.
x = 0.019 .
2
Here, x is the gross annual premium the insur
FIN 3220A Actuarial Models I
First Term 2005-2006
Solutions to Assignment 4
1.
For this policy, the loss-at-issue random variable is
L = v K +1 x aK +1 = 1 + x
d
K +1 x
v
d
The mean and variance of the loss-at-issue are
0.019
0.019
E ( L ) = 1 + x A
FIN 3220A Actuarial Models I
First Term 2005-2006
Assignment 3
Hand in the solutions on or before 16 November 2005.
1.
A 3-year life annuity-due to (x) is defined by the following table:
Year t
0
1
2
Amount of Payment
1
2
3
px+t
0.80
0.75
0.50
You are giv
FIN 3220A Actuarial Models I
First Term 2005-2006
Solutions to Assignment 3
1.
The present value of payments with the associated probabilities are
Curtate future lifetime
0
Probability
qx = 1 0.8 = 0.2
Present value of payment
1
1
px qx +1 = 0.8 (1 0.75 )
FIN 3220A Actuarial Models I
First Term 2005-2006
Solutions to Assignment 2
1.
Let Z be the random variable of the present value of benefit. Since i = 0, we have
with probability 0 q30 = 0.1
b1
Z = 10 b1
0
with probability 1 q30 = 0.9 0.6 = 0.54
with prob
FIN 3220A Actuarial Models I
First Term 2005-2006
Assignment 1
Hand in the solutions on or before 6 October 2005.
1.
100 x
for 0 x 100 . Calculate FX(75), fX(75)
10
You are given the survival function s X ( x ) =
and (75).
2.
You are given the survival fu
FIN 3220A Actuarial Models I
First Term 2005-2006
Solutions to Assignment 1
1.
The survival function is s X ( x ) =
100 x
for 0 x 100. Hence we have
10
FX ( 75 ) = 1 s X ( 75 ) = 1
d
sX ( x )
dx
x = 75
f X ( 75 ) =
( 75 ) =
2.
100 75 1
=,
10
2
1
1
=
=