Critical Analysis
1
You are given the following information for a three-decrement model:
● qx’(1) = 0.10 and is uniformly distributed within each year of age
● qx’(2) = 0.08 and occurs at time 0.6 in each year
● qx’(3) = 0.21 and has a split distribution, half of the impact occurs at time 0.25 in each year and the other half of the impact is uniformly distributed
between time 0.5 and time 1.0
Determine qx(1) .
2
- You are given the following information for a joint life model: • There are exactly three states in the model i. State 0 = Both individuals are alive ii.
State 1 = Exactly one individual is alive iii. State 2 = Both individuals are dead • The two lives are independent i. One individual is 60 years old ii. The
other individual is 75 years old • ?60:75 0,0 1 = 0.5 • ?60+?:75+? 0,2 = 0.05 for 0 ≤ t ≤ 1
Calculate ?60+?:75+? 0,1 as a constant force of transition for 0 ≤ t ≤ 1.
3-
- Z is the present-value random variable for an insurance on the lives of two individuals, Juan and Angela. You are given the following information: • The
insurance benefits are payable at the moments of death • The benefit is $1000 if Angela is alive when Juan dies • The benefit is $10,000 if Juan is already
dead when Angela dies • If Angela dies before Juan, there is no benefit payment • Angela’s survival function follows lx = 100*(100 – x), for 0 ≤ x ≤ 100 •
Juan’s survival function follows lx = 100*(100 – y), for 0 ≤ y ≤ 100 • Angela is 80 years old • Juan is 96 years old • = 0
Calculate the expected value of Z.
Sample Solution