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MATH 471: Actuarial Theory I
Markov Models: Lecture Examples
1. Consider a homogeneous Markov Chain, where an individual can be in one
of two states during the day: State 0 = healthy and State 1 = sick.
The transition matrix is:
Q
=
±
0
.
85 0
.
15
0
.
30 0
.
70
¶
Assume all transitions between states occur at the end of the day.
Given an individual is healthy today (time 0), what is the probability that
she will be healthy.
..
(a) one day from now?
(b) two days from now?
(c) both one day from now and two days from now?
1
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View Full Document 2. Redo Example 1, except now assume a nonhomogeneous Markov Chain
with transition matrices:
Q
0
=
±
0
.
85 0
.
15
0
.
30 0
.
70
¶
Q
1
=
±
0
.
90 0
.
10
0
.
35 0
.
65
¶
2
Dead (2):
(i) The annual transition matrix is given by:
Q
=
0
.
70 0
.
20 0
.
10
0
.
10 0
.
65 0
.
25
0
0
1
(ii) There are 100 lives at the start, all Healthy. Their future states are
independent.
Calculate the variance of the number of the original 100 lives who die
within the ﬁrst two years.
3
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This note was uploaded on 05/18/2011 for the course MATH 472 taught by Professor Zhu during the Spring '08 term at University of Illinois, Urbana Champaign.
 Spring '08
 Zhu
 Math

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