difference in terminal and initial reserve?

[Thomas H]

Is there a difference in the meanings of terminal reserve and initial reserve? If so, what's the difference?

[wat]

Originally Posted by Thomas H

Is there a difference in the meanings of terminal reserve and initial reserve? If so, what's the difference?

Yes.

Terminal reserve (of time t) refers to "the reserve at the end of the period (at time t)".

Initial reserve refers to "the reserve at the beginning of the period".

If you let IV(t) := Initial reserve, TV(t) := Terminal Reserve and P(t) = Premium, then

TV(t-1) + P(t) = IV(t).

The formula above states that the initial reserve equals the terminal reserve from the prior period plus the premium for the current period.

[krzysio]

Originally Posted by wat

Yes.

Terminal reserve (of time t) refers to "the reserve at the end of the period (at time t)".

Initial reserve refers to "the reserve at the beginning of the period".

If you let IV(t) := Initial reserve, TV(t) := Terminal Reserve and P(t) = Premium, then

TV(t-1) + P(t) = IV(t).

The formula above states that the initial reserve equals the terminal reserve from the prior period plus the premium for the current period.

You are right, but you will confuse some readers: TV(t-1) is at time t, so it is denoted by t_V. Terminal reserve is t_V. Initial reserve is t_V + premium. Terminal reserve is calculated at the last nanosecond of the last day of a policy year, and initial reserve is calculated at the first nanosecond of the first day of a policy year, immediately after the premium arrives.

Yours,
Krzys'

[wat]

Originally Posted by krzysio

You are right, but you will confuse some readers: TV(t-1) is at time t, so it is denoted by t_V. Terminal reserve is t_V. Initial reserve is t_V + premium. Terminal reserve is calculated at the last nanosecond of the last day of a policy year, and initial reserve is calculated at the first nanosecond of the first day of a policy year, immediately after the premium arrives.

Yours,
Krzys'

Dr. O,

When you say "initial reserve", what period (i.e., initial reserve for year ___) are you referring to? Because my notation seemed to be consistent with the concept that the initial reserve for any year is the sum of the premium applicable for that year plus the terminal reserve at the end of the prior year.

By the way, Course 7 in Chicago in December was a great experience, and it's a shame to see that opportunity falling by the wayside for the SOA exams.

[krzysio]

Originally Posted by wat

Dr. O,

When you say "initial reserve", what period (i.e., initial reserve for year ___) are you referring to? Because my notation seemed to be consistent with the concept that the initial reserve for any year is the sum of the premium applicable for that year plus the terminal reserve at the end of the prior year.

You have the terminology correct, this is exactly how it works.

Yours,
Krzys'