STAT 4004 Actuarial Science
Tutorial 5
ZHENG,Xunze
Department of Statictics
The Chinese University of Hong Kong
Oct. 20, 2014
*Supplementary material:
Life insurance (or commonly life assurance, especially in the Commonwealth) is a contract between an in
STAT 4004 Mid—Term Test October 15. 2014
Time allowed: 2 hours
Marks distribution: 10 marks for each question
1. An investment fund accumulates with force of interest
K
6‘=1+(1—t)K>
0.
for 0 S t S 1. At time zero there is 100,000 in the fund. At time t =
3. Survival Distributions and Life Tables
3.1. Probability for the Age-at-death
Dene X the age-at-death of a new born baby
X is a continuous random variable
To describe X, we can use
(a) the cumulative distribution of X
F (x) = Pr(X x)
(b) the density
2. Theory of Interest
2.1. The eective rate of interest
Consider a person invest an amount of money in a saving account at
a bank
the initial amount of money invested is called the principal
the total amount received after a period of time is called the
4. Life Insurance
4.1. Insurances Payable at the Moment of Death
bt
6
x+t
death
x
policy issued
bt : benet function
We are not interested in bt itself but the present value when the
policy issued
vt : discount function
Dene the present value function
5. Life Annuities
5.1. Introduction
A life annuity is a series of payments made continuously or at
equal intervals while a given life survives
Annuity-due: payments made at the beginning of the payment
intervals
annuity-immediate: payments made at the
STAT 4004 Assignment 3
Due: November 18, 2015
1. For a 10-year term insurance of 1000 on (x)with benet payable at the moment
of death:
(a)
t =
0.04 0 < t < 5
0.06 t > 5
t =
0.06 0 < t < 5
0.08 t > 5
(b)
Calculate the single benet premium for this insuranc
STAT 4004 Assignment 1
Due: October 2, 2015
1. Suppose the nominal rate of interest convertible monthly is 7%. Find the equivalent
(a) eective rate of interest
(b) nominal rate of discount convertible quarterly
(c) force of interest, assuming it is consta
STAT 4004 Suggested Solution to Assignment 2
Fall 2015
1
f ( x) s '( x)
(a)
x
d
exp
dx
1
x
(b)
( x)
x
exp
f ( x)
s( x)
1
x
(c)
2
2 5
s (5)
exp
s (2)
(a)
FK x y Pr K x y
y 1
qx
s x s x y 1
s x
y 1 , for y 0,1, ,99 x
100 x
STAT 4004 Assignment 2
Due: October 16, 2015
1. Suppose the survivor function of the newborn lifetime X is given by
s(x) = exp
x
,x > 0
Find
(a) the density function of X
(b) the hazard function of X
(c) the probability that X is alive at 5 given X > 2
2
STAT 4004 Suggested Solution to Assignment 1
Fall 2015
1
(a)
i 1 i12
(12)
12
1
1 0.07 1
12
12
7.23%
(b)
(c)
d (4) 4 1 (1 i ) 4
6.92%
1
ln 1 i
6.98%
2
(a)
1
d ( 2)
2
2
e0.06
d (2) 2 1 e
5.91%
(b)
3
0.06
2
i (4) 4 e 4 1
6.05%
0.06
For Fund A,
a
STAT 4004 Suggested Solution to Assignment 2
Fall 2012
1
f ( x) s '( x)
(a)
x
d
exp
dx
1
x
x
exp
1
(b)
(c)
2
f ( x) x
( x)
s ( x)
2 5
s (5)
exp
s (2)
(a)
FK x y Pr K x y
y 1
qx
s x s x y 1
s x
y 1
100 x , for y 0,1, ,99 x
1
SOCIETY OF ACTUARIES
EXAM C CONSTRUCTION AND EVALUATION OF ACTUARIAL MODELS
EXAM C SAMPLE SOLUTIONS
The sample questions and solutions have been modified over time. This page indicates
changes made since January 1, 2014.
June 2016
Question 266 was moved t
SOCIETY OF ACTUARIES
EXAM C CONSTRUCTION AND EVALUATION OF ACTUARIAL MODELS
EXAM C SAMPLE QUESTIONS
The sample questions and solutions have been modified over time. This page indicates
changes made since January 1, 2014.
June 2016
Question 266 was moved t
Tables for
Exam C
The reading material for Exam C 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
Construction and Evaluation of Actuarial Models ExamOctober 2016
The Construction and Evaluation of Actuarial Models exam is a three-and-a-half hour exam that
consists of 35 multiple-choice questions and is administered as a computer-based test.
For addit
CONSTRUCTION AND EVALUATION OF ACTUARIAL MODELS STUDY NOTE
REPLACEMENT PAGES FOR SECTION 16.5.3 FROM
LOSS MODELS: FROM DATA TO DECISIONS, FOURTH EDITION
by
Stuart A. Klugman
Copyright 2016 Society of Actuaries
The Education and Examination Committee provi