Duc Thinh Vu
Active Member
Hello,
I would like to ask a question concerning the meaning of reserve and the cost of setting up reserve when we do the profit testing in term life insurance.
For example, we want to calculate the profit for the year from t = 0 to t = 1. The calculation is done at time t = 1
In the book "Actuarial Mathematics for Life contingent risks" of Mr. Dickson, he stated that we have to take into account of the reserve.
In details, he said (assume that the client buys the contract at the age of 60)
My questions are:
1. The insurance company does not have to hold reserve for the ended contracts. So in reality, I think it only needs to hold a reserve of 1V.p60 = 405.95 instead of 1V = 410.05. Holding an un-necessary amount of reserve will be costly for the insurance company.
Am I right or wrong ?
2. I think, to setup a reserve of 410.05, it should also cost the insurance companies 410.05.
But why do we only need 405.95 to setup an amount of reserve of 410.05 ? I'm very confusing about 2 terms "Reserve" and "Cost of setting up the reserve"
3. I want to take into account also the lapse rate in calculating the cost of setting up reserve for more realistic profit testing.
(say, for example, the lapse rate is 10%. So the cost of setting of a reserve of 1V = 410.05 is actually 1V.p60.(1-lapse_rate) ).
Am I right ?
I would like to thank you very much for your help! I'm struggling for 1 week but still can't understand the concept.
I would like to ask a question concerning the meaning of reserve and the cost of setting up reserve when we do the profit testing in term life insurance.
For example, we want to calculate the profit for the year from t = 0 to t = 1. The calculation is done at time t = 1
In the book "Actuarial Mathematics for Life contingent risks" of Mr. Dickson, he stated that we have to take into account of the reserve.
In details, he said (assume that the client buys the contract at the age of 60)
We need to include in our profit test the cost of assigning these amounts. To see how to do this, consider, for example, the reserve required at time 1, 1V = 410.05.
This amount is required for every policy still in force at time 1. The cost to the insurer of setting up this reserve is assigned to the previous time period and this cost is: 1V . p60 = 410.05 × (1 - 0.01) = 405.95
The cost includes the factor p60 since all costs relating to the previous time period are per policy in force at the start of that time period, that is, at time 0. The expected proportion of policyholders surviving to the start of the following time period, i.e. to age 61, is p60
My questions are:
1. The insurance company does not have to hold reserve for the ended contracts. So in reality, I think it only needs to hold a reserve of 1V.p60 = 405.95 instead of 1V = 410.05. Holding an un-necessary amount of reserve will be costly for the insurance company.
Am I right or wrong ?
2. I think, to setup a reserve of 410.05, it should also cost the insurance companies 410.05.
But why do we only need 405.95 to setup an amount of reserve of 410.05 ? I'm very confusing about 2 terms "Reserve" and "Cost of setting up the reserve"
3. I want to take into account also the lapse rate in calculating the cost of setting up reserve for more realistic profit testing.
(say, for example, the lapse rate is 10%. So the cost of setting of a reserve of 1V = 410.05 is actually 1V.p60.(1-lapse_rate) ).
Am I right ?
I would like to thank you very much for your help! I'm struggling for 1 week but still can't understand the concept.