IEOR 4106: Professor Whitt
Lecture Notes, Thursday, February 3
Even More on Markov Chains
Examples
1. A Markov Chain Example in Credit Risk Modeling
See the separate handout, also posted on the web page.
2. Examples 4.1 and 4.4: weather forecasting.
3. Example 4.7: automobile insurance premiums.
This is
the insurance example, Example 4.7
in the textbook. This is a slight simpli
fication of a realistic application of Markov chains. We construct the model by constructing
the transition matrix, given in the book:
P
=
a
0
a
1
a
2
1

a
0

a
1

a
2
a
0
0
.
0
a
1
1

a
0

a
1
0
.
0
a
0
0
.
0
1

a
0
0
.
0
0
.
0
a
0
1

a
0
There are four states: 1
,
2
,
3
,
4, with state 1 being the bonus (good) state. Higher states mean
a worse claim record, but in this case we place an upper limit of 4.
The elements of the 4
×
4 matrix are probabilities:
a
k
is the probability of having
k
accidents
(actually making
k
claims) during the year. The row sums necessarily are 1. The probability
entries
a
k
here are in this case in the book are computed as Poisson probabilities; i.e., then
a
k
=
e

λ
λ
k
k
!
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 Spring '11
 WhitWard
 Markov Chains, Probability theory, Markov chain, steady state probability

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