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An insurance company uses a 4state Markov chain to model transitions of insureds for medical insurance. State 0 = healthy; State 1 = disease 1;...

a.At time 0, 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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9. An insurance company uses a 4—state Markov chain to model transitions of
insureds for medical insurance. State 0 = 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 0
0.2 0.6 0.1 0.1
0 0 0.8 0.2
0 0 0 1 Transitions occur mid-year. For a l-year medical insurance at the end of every year, insureds diagnosed with disease 1 are paid 100; those with disease 2 are paid 200. There is no death benefit. Healthy insureds pay P at 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 0, 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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