ACSC/STAT 4720, Life Contingencies II
Fall 2016
Toby Kenney
Homework Sheet 1
Due: Friday 30th September: 12:30 PM
Basic Questions
1. An insurance company is developing a new policy. The policy considers 4 states: Employed, On leave, Retired,
and Dead. The

ACSC/STAT 4720, Life Contingencies II
FALL 2015
Toby Kenney
Sample Midterm Examination
Model Solutions
This Sample examination has more questions than the actual midterm, in order to cover a wider
range of questions. Estimated times are provided after eac

ACSC/STAT 4720, Life Contingencies II
FALL 2015
Toby Kenney
Sample Final Examination
Model Solutions
1. An individual aged 42 has a current salary of $76,000 for the coming year. The salary scale is sy = 1.05y .
Estimate the individuals final average sala

ACSC/STAT 4720, Life Contingencies II
Fall 2015
Toby Kenney
Homework Sheet 3
Model Solutions
Basic Questions
1. An individual aged 37 has a current salary of $116,000. The salary scale is sy = 1.04y . Estimate the
individuals final average salary (average

7
Smoothing
7.1
Probabilistic Solution
The smoothing problem seeks to determine the conditional pdf
p(x0 , . . . , xN |YN ).
Using Bayes theorem, this conditional density function can be represented,
p(x0 , . . . , xN |YN ) =
p(YN |x0 , . . . xN )p(x0 , .

ACSC/STAT 3720, Life Contingencies I
Winter 2015
Toby Kenney
Homework Sheet 7
Model Solutions
Basic Questions
1. An insurance company sells 400 whole life insurance policies with annual premiums and
benefits to select lives aged 36. The death benefit on t

ACSC/STAT 3720, Life Contingencies I
Winter 2015
Toby Kenney
Homework Sheet 6
Model Solutions
Basic Questions
1. An insurer issues 5,000 whole life insurance policies to select lives aged 51. The appropriate
interest rate is i = 0.06. The company calculat

ACSC/STAT 3720, Life Contingencies I
WINTER 2015
Toby Kenney
Sample Midterm Examination
This Sample examination has more questions than the actual midterm, in order to cover a wider
range of questions. Estimated times are provided after each question to h

ACSC/STAT 3720, Life Contingencies I
Winter 2015
Toby Kenney
Homework Sheet 8
Model Solutions
Basic Questions
1. A woman aged 36, who is a select life on Table 1 buys a 10-year term insurance policy with
a death benefit of $600,000. (The policy uses a net

ACSC/STAT 3720, Life Contingencies I
Winter 2015
Toby Kenney
Homework Sheet 5
Model Solutions
Basic Questions
1. An insurance company offers a 10-year endowment policy with benefit $700,000 payable either
at the end of the year of death, or at the end of

ACSC/STAT 3720, Life Contingencies I
WINTER 2015
Toby Kenney
Sample Final Examination Model Solutions
1. For a life aged 32, for whom Table 1 is appropriate, an insurance company provides a whole
life insurance policy with annual premiums $3,803 and death

STAT 4390/5390, OCEAN 4210/5210
Assignment 6
(due Monday, March 6, 2017)
1. Derive the spectral density, f (), for the AR(1) model, xt = 1 xt1 +
wt . Do this two ways: (i) using the result in Property 4.3 (i.e. Spectral
Density of an ARMA process) in text

Time Series Analysis
STAT 4390/5390
OCEAN 4210/5210
Assignment 3: Due Wed 1 Feb, 2017
1. Consider the AR(1) model xt = 1 xt1 +wt where wt N ID(0, w2 ).
Show that for | < 1, the auto-covariance is
(h) =
2t
.
1 2
1
w2 h
(Note that for large t, this reduces

Time Series Analysis: STAT 4390/5390 OCEAN 4210/5210
Assignment 4: Due Mon 13 Feb, 2017
Time Series data for the annual global air temperature for the period 1951-1989 is
provided on the website. Our goal is to fit a linear trend to these data and assess

Time Series Analysis
STAT 4390/5390
OCEAN 4210/5210
Assignment 2: Due Wed 25 January, 2017
1. Question 1.13 from Shumway and Stoffer textbook
(6
2. Consider the white noise process wt , and a 5-point moving av- (6)
erage process vt of it.
(a) Determine th

STAT 4390/5390, OCEAN 4210/5210
Assignment 7 (due Wednesday, March 15, 2016)
The purpose of this assignment is to carry out a spectral analysis in practice. Posted on the website is a text file. It contains two sea level time series
from Tracadie Bay, P.E

ACSC/STAT 4720, Life Contingencies II
Fall 2015
Toby Kenney
Homework Sheet 5
Model Solutions
Basic Questions
1. An insurance company sells a 5-year annual life insurance policy to a life aged 41, for whom the lifetable below
is appropriate.
x
41
42
43
44

ACSC/STAT 4720, Life Contingencies II
Fall 2015
Toby Kenney
Homework Sheet 4
Model Solutions
Basic Questions
1. A life aged 46 has mortality given in the table below. The yield rate is in another table below
x
46
47
48
49
50
lx
10000.00
9998.99
9997.89
99

ACSC/STAT 4720, Life Contingencies II
FALL 2015
Toby Kenney
Sample Midterm Examination
This Sample examination has more questions than the actual midterm, in order to cover a wider
range of questions. Estimated times are provided after each question to he

ACSC/STAT 4720, Life Contingencies II
Fall 2016
Toby Kenney
Homework Sheet 2
Due: Friday 5th October: 12:30 PM
Basic Questions
1. The following is a standard multiple decrement table giving probabilities of death and surrender for a life
insurance policy:

ACSC/STAT 4720, Life Contingencies II
Fall 2016
Toby Kenney
Homework Sheet 1
Model Solutions
Basic Questions
1. An insurance company is developing a new policy. The policy considers 4 states: Employed, On leave, Retired,
and Dead. The transition diagram i

ACSC/STAT 4720, Life Contingencies II
Fall 2016
Toby Kenney
Homework Sheet 2
Model Solutions
Basic Questions
1. The following is a standard multiple decrement table giving probabilities of death and surrender for a life
insurance policy:
x
53
54
55
56
57

ACSC/STAT 4720, Life Contingencies II
Fall 2015
Toby Kenney
Homework Sheet 1
Due: Friday 2nd October: 12:30 PM
Basic Questions
1. An insurance company is developing a new policy. The policy considers 4 states: Healthy, Sick, Disabled, and
Dead. The transi

ACSC/STAT 4720, Life Contingencies II
Fall 2015
Toby Kenney
Homework Sheet 3
Due: Friday 16th October: 12:30 PM
Basic Questions
1. An individual aged 37 has a current salary of $116,000. The salary scale is sy = 1.04y . Estimate the
individuals final aver

ACSC/STAT 4720, Life Contingencies II
Fall 2015
Toby Kenney
Homework Sheet 4
Due: Friday 13th November: 12:30 PM
Basic Questions
1. A life aged 46 has mortality given in the table below. The yield rate is in another table below
x
46
47
48
49
50
lx
10000.0

ACSC/STAT 4720, Life Contingencies II
Fall 2015
Toby Kenney
Homework Sheet 5
Due: Friday 20th November: 12:30 PM
Basic Questions
1. An insurance company sells a 5-year annual life insurance policy to a life aged 41, for whom the lifetable below
is appropr

ACSC/STAT 4720, Life Contingencies II
Fall 2015
Toby Kenney
Homework Sheet 6
Due: Friday 2nd October: 12:30 PM
Basic Questions
1. A policyholder aged 54 buys a 10-year type B universal life insurance policy. The additional death benefit
is $150,000. The p

ACSC/STAT 4720, Life Contingencies II
Fall 2015
Toby Kenney
Homework Sheet 2
Due: Friday 7th October: 12:30 PM
Basic Questions
1. The following is a multiple decrement table giving probabilities of death and surrender for a life insurance
policy:
x
53
54

ACSC/STAT 4720, Life Contingencies II
Fall 2015
Toby Kenney
Homework Sheet 7
Due: Friday 2nd October: 12:30 PM
Basic Questions
1. An equity-linked insurance policy has the following properties:
Annual premiums are $8,000.
Expense charges are 10% of the

ACSC/STAT 4720, Life Contingencies II
Fall 2015
Toby Kenney
Homework Sheet 7
Model Solutions
Basic Questions
1. An equity-linked insurance policy has the following properties:
Annual premiums are $8,000.
Expense charges are 10% of the first premium and