ACTUARIAL MATHEMATICS 2 ASSINGMENT
NAME: OSCAR COLLINS ODHIAMBO
ADM: W132/G/5487/22
Health insurance in Kenya
Solution
To solve the problem we can use the multiple state model with the given transition intensities to
calculate the probabilities
We can use the following formula to calculate the probabilities
P(H) = 1/1+0.05 + 0.07 + 0.1
=1/1.22
=0.8165
P(S) = 0.07P(H)/1+0.25+0.1
=0.07*0.8165/1.35
=0.0499
P(D) = 0.05*P(H) + 0.1*P(S)/1+0.25 + 0.1
=0.05*0.8165 + 0.1*0.0499/1.35
0.0326
Now let us calculate the probabilities of the policy holder being sick at exactly at age 52 and
being dead at age 52
Probability of being sick at age 52
P(S) = 0.0499
Probability of being dead at age 52
P(D) = 0.0326
1|Page
NAME: OSCAR COLLINS ODHIAMBO
ADM: W132/G/5487/22
Health insurance in Kenya
Solution
To solve the problem we can use the multiple state model with the given transition intensities to
calculate the probabilities
We can use the following formula to calculate the probabilities
P(H) = 1/1+0.05 + 0.07 + 0.1
=1/1.22
=0.8165
P(S) = 0.07P(H)/1+0.25+0.1
=0.07*0.8165/1.35
=0.0499
P(D) = 0.05*P(H) + 0.1*P(S)/1+0.25 + 0.1
=0.05*0.8165 + 0.1*0.0499/1.35
0.0326
Now let us calculate the probabilities of the policy holder being sick at exactly at age 52 and
being dead at age 52
Probability of being sick at age 52
P(S) = 0.0499
Probability of being dead at age 52
P(D) = 0.0326
1|Page
