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An insurance company uses a 4-state Markov chain to model transitions of insureds for medical insurance . State O = healthy ; State 1 = disease 1 ;...

Please answer the following question with all steps for parts a, b, and c.

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q9.png

9. An insurance company uses a 4-state Markov chain to model transitions of
insureds for medical insurance . State O = healthy ; State 1 = disease 1 ; State
2 = disease state 2 ( advanced stage of disease 1 ) ; state 3 = dead .
The one- year transitions matrix is :"
0 . 7
0 . 2
0 . 1
O
0 . 2
0. 6
0 . 1
0 . 1
O
O
0 . 8
0 . 2
O
1
Transitions occur mid - year .
For a 3 - year medical insurance at the end of every year , insureds diagnosed
with disease I are paid 100 ; those with disease 2 are paid 200 . There is no
death benefit . Healthy insureds pay Pat the beginning of the year .
At the beginning of year 2 , 15% of healthy insureds lapse . 10% of disease 1
insureds also terminate*
Questions :"
a . At time O , there are 100 policies , all healthy , in force . Calculate the
number in force at time 3 .
b. Calculate the expected present value at issue of all benefits payable*
during the 3 year term of the insurance . Assume 5% interest .
C . Calculate P using the equivalence principle .

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