ACT455H1S - TEST 2 - MARCH 17, 2009 Write name and student number on each page. Write your solution for each question in the space provided. For the multiple decrement questions, it is always assumed that decrements are independent of one another unless i
12.
A new disease has the following characteristics: (i) Once an individual contracts the disease, each year they are in only one of the following states with annual treatment costs as shown: State Acutely ill In remission Cured or dead Annual Treatment C
ACT455H1S - TEST 1 - FEBRUARY 12, 2008 Write name and student number on each page. Write your solution for each question in the space provided. For the multiple decrement questions, it is always assumed that decrements are independent of one another unles
ACT455H1S - TEST 1 - FEBRUARY 6, 2007 Write name and student number on each page. Write your solution for each question in the space provided. For the multiple decrement questions, it is always assumed that decrements are independent of one another unless
ACT455H1S - TEST 2 - MARCH 25, 2008 Write name and student number on each page. Write your solution for each question in the space provided. For the multiple decrement questions, it is always assumed that decrements are independent of one another unless i
ACT455H1S - TEST 2 - MARCH 20, 2007 Write name and student number on each page. Write your solution for each question in the space provided. For the multiple decrement questions, it is always assumed that decrements are independent of one another unless i
ACT455H1S - TEST 1 - FEBRUARY 11, 2009 Unless indicated otherwise, assume that decrements are independent of one another. Write name and student number on each page. Write your answer for each question beside the question number.
2 2 2 2
1. A three decrem
24.
For a perpetuity- immediate with annual payments of 1: (i) The sequence of annual discount factors follows a Markov chain with the following three states: State number Annual discount factor, v (ii) 0 0.95 1 0.94 2 0.93
The transition matrix for the a
MARKOV CHAINS - SUPPLEMENTARY PROBLEM SET
MARKOV CHAINS - ADDITIONAL PROBLEMS
1. A two-state homogeneous Markov chain is being used to model the transitions between days with rain (R) and without rain (N). You are given UVV & UR R (& . (a) If it is rainin
9.
Lucky Tom finds coins on his way to work at a Poisson rate of 0.5 coins/minute. The denominations are randomly distributed: (i) (ii) (iii) 60% of the coins are worth 1 each 20% of the coins are worth 5 each 20% of the coins are worth 10 each.
Calculate
jan24-06 Page 7
7.
For a multiple decrement table, you are given: (i) Decrement 1 is death, decrement 2 is disability, and decrement 3 is withdrawal. q60(1) = 0.010 q60(2 ) = 0.050 q60(3 ) = 0100 . Withdrawals occur only at the end of the year. Mortality
ACT455H1S - TEST 3 - APRIL 10, 2007 Write name and student number on each page. Write your solution for each question in the space provided. 1. A homogeneous Poisson Process has a rate of - " per period. Find each of the following. (a) IR #lR " " (b) IR "
ACT455H1S - TEST 3 - APRIL 8, 2008 Write name and student number on each page. Write your solution for each question in the space provided. 1. Cars cross a certain point (point x) in the highway according to a Poisson process with a rate of - oe $ per min
6.
Insurance losses are a compound Poisson process where: (i) The approvals of insurance applications arise in accordance with a Poisson process at a rate of 1000 per day. Each approved application has a 20% chance of being from a smoker and an 80% chance
10.
For a fully discrete whole life insurance of 1000 on (x), you are given: (i) (ii) (iii) (iv) (v) (vi) (vii) (viii)
G = 30 ek ck i
5, 0.02, 0.05 75 0.013 0.05 25.22
k 1, 2,3,. k 1, 2,3,.
4 CV d 3 w 3
qx qx
3 AS
If withdrawals and all expenses for year
29.
A machine is in one of four states (F, G, H, I) and migrates annually among them according to a Markov process with transition matrix: F F G H I 0.20 0.50 0.75 1.00 G 0.80 0.00 0.00 0.00 H 0.00 0.50 0.00 0.00 I 0.00 0.00 0.25 0.00
At time 0, the machi
15.
In a double decrement table: (i) (ii) (iii) (iv) (v)
b l30 g = 1000
q301g = 0100 . b q302 g = 0.300 b
1 1 q30 = 0.075
bg
b l32 g = 472
b2 Calculate q31 g .
(A) (B) (C) (D) (E) 0.11 0.13 0.14 0.15 0.17
COURSE/EXAM 3: MAY 2000
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197. For a special 3-year term insurance on ( x ) , you are given:
(iv) (v) (vi) Z is the present-value random variable for this insurance.
qx
k
0.02( k 1) ,
k
0, 1, 2
The following benefits are payable at the end of the year of death: k 0 1 2
bk
1
300 35
38.
For a triple decrement model: (i) x 63 64 65 (ii) (iii) qxb1g 0.02000 0.02500 0.03000 q b 2g x 0.03000 0.03500 0.04000 q b3g x 0.25000 0.20000 0.15000
b1 q65g = 0.02716
Each decrement has a constant force over each year of age.
b1 Calculate 2 q64g .
(
27.
(50) is an employee of XYZ Corporation. Future employment with XYZ follows a double decrement model: (i) (ii) (iii) (iv) (v) Decrement 1 is retirement.
1 50
t
0.00 0.02
0 t 5 t
5
Decrement 2 is leaving employment with XYZ for all other causes.
2 50
t