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

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

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