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engelbmj
January 14th 2007, 03:32 PM
I'm currently using the 2007 Actex CAS Exam 3 study manual, written by Hasset et al. I'm working through module 9 (Benefit Reserves), and have found a particular Reserve notation that is a bit confusing.

I will use the notation [t]V[x] to represent the reserves at time t for insurance that is sold to (x). In actuarial notation, the t would be a leading subscript, and x would be a trailing subscript. I can't denote bars, so let's just assume we're dealing with fully discrete reserves.

In some of the questions where insurance is sold to (x), I've noticed that both [t]V and [t]V[x] are used to refer to a future reserve at time t. What is the difference between the two? When these are used, it seems like [t]V[x] refers to a reserve at time t where benefits and premiums are level at 1 (ie normalized), wheres [t]V refers to the reserve at time t with benefit and premium levels and schedules as they have been defined in the question.

For example, if you have this study manual, Example (9.53) on pg. 33 of module 9 defines these 2 reserve notations. The [t]V[x] is the reserve with benefits and premiums normalized, whereas [t]V is the "real" reserve.

If anyone can help out, it would be appreciated. Another follow up question I would have is this: is this convention used for reserves in the continuous case too? Thanks.

- Matt

ctperng
January 14th 2007, 04:45 PM
I'm currently using the 2007 Actex CAS Exam 3 study manual, written by Hasset et al. I'm working through module 9 (Benefit Reserves), and have found a particular Reserve notation that is a bit confusing.

I will use the notation [t]V[x] to represent the reserves at time t for insurance that is sold to (x). In actuarial notation, the t would be a leading subscript, and x would be a trailing subscript. I can't denote bars, so let's just assume we're dealing with fully discrete reserves.

In some of the questions where insurance is sold to (x), I've noticed that both [t]V and [t]V[x] are used to refer to a future reserve at time t. What is the difference between the two? When these are used, it seems like [t]V[x] refers to a reserve at time t where benefits and premiums are level at 1 (ie normalized), wheres [t]V refers to the reserve at time t with benefit and premium levels and schedules as they have been defined in the question.

For example, if you have this study manual, Example (9.53) on pg. 33 of module 9 defines these 2 reserve notations. The [t]V[x] is the reserve with benefits and premiums normalized, whereas [t]V is the "real" reserve.

If anyone can help out, it would be appreciated. Another follow up question I would have is this: is this convention used for reserves in the continuous case too? Thanks.

- Matt

Usually the context should make that clear. I don't have your manual, but I guess you are safe to assume that: according to AM = Actuarial Mathematics(second edition) table 7.2.1 for fully discontinuou benefit reserves (p. 212) and table 7.4.1 for fully discrete benefit reserves (p. 216), the use of subscript x is to refer to age at issue x with unit benefit.

On page 230 of AM, benefit reserves for general insurances are defined, this time without the subscript x. According to the formula, the premiums and benefits are more general.

By the way, you should know there are several variant notations of reserves, depending on the payments scheme or the number of terms.

ctperng

.Godspeed.
January 14th 2007, 05:02 PM