Talks About Pension Mathematics pension mathematics actuary

[actuarymath 1]

I owned a Japanese blog at
http://d.hatena.ne.jp/actuary_math/

Once I posted taking about pension mathematics at
http://d.hatena.ne.jp/actuary_math/20080819

Now I translate it into English as follows because it will somehow server those who studies pension mathematics.

----I will obtain the questioner's consent and publish because the question concerning the pension mathematical principle is received from the reader of the blog, and it did the round trip letter several times (In E-mail).
It would be greatly appreciated if it could help you because there might be similar doubt.
leaning though it has been passed by the life insurance mathematical principle and there is knowledge at a constant level the questioner.

< points of concern >
(1)I must consent for the examination of not the specialist of the pension mathematical principle but the pension mathematical principle and ten years or more from now it is ahead.
(Though the text etc. of the pension mathematical principle have been reviewed because the actuary examination has been guided afterwards. )
(2)Moreover, I must pardon digging corporate pension accounting/retirement benefit accounting of corporate pension accounting/retirement benefit accounting because of unprofessional it down though it writes at the end of a series of communication.
(3)An unrelated part to the question like the greeting etc. is omitted. Moreover, it changes within the range where the meaning of a so-called platform dependent character like the encircled number etc. etc. is not changed.

Question 1
Frequently I am sorry. Though I would like you to teach when it is understanding.

As for the comprehensive insurance open fee type of the pension mathematical
principle, it is.
There are four patterns in the comprehensive insurance open fee type when the
system is introduced. (F_n=0 when introducing it)

(1)It supplies to the retiree, and the work period of the past is
totaled.
P_n^{(1)}=\frac{S^p+S^a+S^f-F_n}{G^a+G^f}
(\frac{x}{y}=x/y as is same as follows)

(2)It doesn't supply even to the retiree, and the work period of the
past is not totaled.
P_n^{(2)}=\frac{S^a+S^f-F_n}{G^a+G^f}

(3)The work period on the past of the insurant of in service is not
totaled.
P_n^{(3)}=\frac{S^a_{FS}+S^f-F_n}{G^a+G^f}

(4)The object person of the supply is limited only to the insurant in
the future.
P_n^{(4)}=\frac{S^f-F_n}{G^a+G^f}

It is.

Q1 . Is to regularity this pattern?
As well as P_n^{(1)} it when it becomes regular Is it P_n=\
frac{S^p+S^a+S^f-F_n} {G^a+G^f}?
Or, is the pattern of (1) ?(4) applied even if becoming regular?

By the way,
In the 13th line at the page 107 in
http://www.su-jine.net/
I saw "the premium will be also applied as same as that was fiexd at the beginning."
and I thought it was not as same as P_n^{(1)}.
Nevertheless in the formula (5.87) at the page 108 in the same book P_n^{(1)} was written.
So I was very confused.

Q2 . V of (1)-(4) is not described in the textbook, and the expression of V is not understood and it embarrasses it.
Respectively
Will it be V=S^p+S^a+S^f-P(G^a+G^f) (As for (1)-(4), P is P_n^{(1)}-P_n^{(4)} respectively)?
Or,do it become
(1)V_n=S^p+S^a+S^f-P_n^{(1)}(G^a+G^f)
(2)V_n=S^a+S^f-P_n^{(2)}(G^a+G^f)
(3)V_n=S^a_{FS}+S^f-P_n^{(3)}(G^a+G^f)
(4)V_n=S^f-P_n^{(4)} (G^a+G^f)?
By the way, when it can be taught how to do F, it is very welcome.

Answer 1

>saying that "(close type) aggregate cost method" (text p76-p79 (The textbook of IAJ (the institute of actuaries of Japan) is indicated: It is the same as follows))
When "Comprehensive insurance open fee method" (text p87-p91) is confused, it is feared.
"Close type comprehensive insurance fee method" is only indicated in case of "Aggregate cost method".

Insurance is not defined by "Progression" like F_n about "Type of open" comprehensive insurance fee method in the book (text , http://www.su-jine.net/ and http://www.su-jine.net/) for me, and insurance steadies.
Or, a page concerned is scanned if it is possible to do if it is a book other than and there is such a description and it is welcome when sending it.

>
http://www.su-jine.net/
As for "The premium provided when the system of the premium is introduced will be applied regardless of the passage in fiscal year", insurance is thought by the 13th line of P107 of the book > that it means the insurance decided once is applied every year (Special insurance is none) during year by each of the four patterns though differs.

The constant insurance is different according to each pattern.
http://www.su-jine.net/
Because this value is different by each pattern, insurance is different though it drinks and there is ^{o}F about the formula (5.87).

Reserve fund = liability reserve (If you do not think about the profit loss
from the difference of quotation profit etc.) concrete (stationary state)
can be requested by applying limit equation C+d*F=B.

Question 2

Q1.
http://www.su-jine.net/
There is insurance of the stationary state of the comprehensive
insurance open fee type according to drinking p108 when it is
expressible like expression (5.87) ^{o} P=\frac{S^p+S^a+S^f-^oF} {G^a+G^f}.

Possibly
Insurance is thought to mean the insurance decided once is applied every year (Special insurance is none) during year by each pattern of four > though differs.
The explanation thinks that it doesn't attach.
Does it settle down in one pattern four patterns in the stationary state?(Do it become an expression (5.87) momentarily became regular?)

Q2.
> can be requested by applying limit equation C+d*F=B.
What meaning is of the profit loss from the difference of quotation profit etc. not to think if and > profit loss from the difference of quotation profit of the point etc. are not thought when and F=V are approved?
Will F=V be mean no regular approval if the thing doesn't advance to the last according to the assumed interest rate and the assumed rate of mortality when F and V are calculated?

Answer 2

The insurance of the stationary state of the comprehensive insurance > open fee type is {} ^{o} expression (5.87) > P=\frac{S^p+S^a+S^f-^oF} {G^a+G^f} It is when expressible like >.
...>.. possibly>
> Insurance is thought to mean the insurance decided once is applied every year (Special insurance is none) during year by each of the four patterns though differs.
I think that the explanation > doesn't attach.
Does it settle down in one pattern the pattern of four > in the stationary state?>
(Do it become an expression (5.87) momentarily became regular?)

Four patterns are not to settle down in one.
(5.87)^{o} P is also different differing in ^{o} F four patterns though it peels off and it is writing by the expression) Thus, it does.
Concretely,

It supplies to > (1) retiree, and the work period of the past is
totaled.
^{o}F=0

It doesn't supply even to > (2) retiree, and the work period of the
past is not totaled.
^{o}F=S^p

The work period on the past of the insurant of in service of > (3) is
not totaled.
^{o}F=S^p+S^a_{PS}

The object person of > (4) supply is limited only to the insurant in
the future.
^{o}F=S^p+S^a

Thus, it does.

What meaning is not to think about > profit loss from the difference of quotation profit etc.
Will F=V be mean no regular approval if the thing doesn't advance according to the assumed interest rate and the assumed rate of mortality when F and V are calculated to the last ?

That.
If the thing doesn't advance according to the assumed interest rate
and the assumed rate of mortality and special insurance is not
received, unsavings debt U=V-F (text p72) is caused.

Question 3
Q.However, only one point
If > special insurance is not received, unsavings debt U=V-F (text p72) is caused.
The collection of special insurance that it is a point is understanding that the past service liability is lost. However, I do not think that there is actually entering of cash.
The one that F is cash (Because it is F=0 and (F_n+C) (1+i) - B=F_{n+1} at the first year) in my understanding reserved with the company, and it is necessary to save the same amount as V.
Moreover, when piling up when the past service liability (henceforth PSL) is introduced in pension system, and matching to V, amount insufficient in V doesn't pile up PSL. PSL will be adjusted to 0 during the future. It is light understanding.
When system is introduced if it is assumed PSL=100 when pension system is introduced in a word, and redeems it in ten years (Hereafter, when writing by the sort).
|[F] 100|[PSL] 100|
In one year
|[PSL] 100/10=10|Special insurance 10|
Near special insurance becomes insurance without the proof of cash.
Then, I think that it is not cash from which F is reserved with
the company.
Is understanding to my F wrong?

Q2 . moreover, why though it is a relating story might is Fackler's reflexive type when there is PSL different in F and V like (F_n+C^n+C^s) (1+i) - B=F_{n+1} and \ (V_n+C^n) (1+i) - B=V_{n+1}, etc.
(In C^n, standard insurance and C^s are special insurances;Because Japanese was not able to be used in diamond Lee's tex notation, the initial of normal and special was taken and it was written though it wrote in C signpost and C special Japanese in the quotation Shasoso original as n and s. )
(It asked and was written in the past of H13(14). )

Answer 3

>, only one point
>> If special insurance is not received, unsavings debt U=V-F (text p72) is caused.
The collection of special insurance is understanding that the past service liability is lost though it is a point >. However, I do not think that there is actually entering of cash.
The one that F is cash (Because it is F=0 and (F_n+C) (1+i) - B=F_{n+1} at the first year) in > my understanding reserved with the company, and it is necessary to save the same amount as V.
When piling up when the past service liability (henceforth PSL) is introduced in pension system, and matching to V, amount insufficient in > and V doesn't pile up PSL. PSL will be adjusted to 0 during the future. It is light understanding.
If it is assumed PSL=100 at > ,in a word, the pension system introduction, and redeems it in ten years (Hereafter, when writing by the sort) When > system is introduced.
|[F] 100|[PSL] 100|
In one year
|[PSL] 100/10=10|Special insurance 10|
It becomes > and special insurance becomes insurance without the
proof of cash.
I think > to be no cash from which F is reserved with the company
then.
Is understanding to > my F wrong?

PSL is not "Pile up" the one.
It recognizes it as a difference between the property (reserve fund)
and the debt (liability reserve).
When it is a presentation example(The liability reserve is not a tile. )


Balance sheet of system introduction
|Part of property|Part of debt|
|Cash (F) 0|Liability reserve (V) 100|
| |Part of net assets|
| |Loss money *100|
| |Part of debt and net assets|
| |100+*100=0|

Sort after one year
|Debit|Credit|
|Cash 10|Special insurance 10 (income account)|
(→ decreases loss money by this ten. )

Balance sheet after one year
|Part of property|Part of debt|
|Cash 10 (F)|Liability reserve (V) 100|
| |Part of net assets|
| |Loss money * 90|
| |Part of debt and net assets|
| |100+*90=10|

It becomes it.

> Q2 . It is (F_n+C^n+C^s) (1+i) - B=F_{n+1}, and moreover, > it is F, V, and Fackler's reflexive type when there is PSL is (V_n+C^n) (1+i) - B=V_{n+1} though it is a relating story why might do you differ like >?>
(In C^n, standard insurance and C^s are special insurances) Please see figure under > (It asked and was written in the past of H13(14)) text p73.
Special insurance doesn't enter the reflexive type of V because the difference between a supply present value and a standard insurance income present value is liability reserves.
On the other hand, because F is the entire reserve fund of the company, it is counted in including special insurance.
(It is thought assumed interest rate = actually that it is an interest rate in this problem, and when the interest rate is actually different from the assumed interest rate, ..only F.. is applied the interest rate actually. )

Question 4
Q1 . Indeed, special insurance has entering of cash. It became study very much.
Not piling up and PSL are that I whether be turning over and read ..PSL.. amount F in a word in a different way as Co loss money or surplus at the beginning of period.
On the other hand, because F is the entire reserve fund of the company, it ..Q2 ".. is counted in including special insurance. "
Because do you turn around to F?
By the way, a similar expression is to the question in the past of H17(2).
F at the time of of the end of fiscal year donates amount that in the under and the amount that falls below constant comparatively correspond to r with V as special insurance in a certain pension system at the time end of next year. This system is a stationary state.
Fiscal year..end..end..show..count..choose.It was, and ..period Hatshara.. donating special insurance in ..assumed interest rate i.. yield on investment j however had the problem of end of fiscal year. In this problem, is it a stationary state and does PSL exist at the beginning of period?The definition of the stationary state : though it must be V=F . However, the limit equation of F and V had been approved just like the stationary state why.
It wrote in (F+C^n- (1+i) (F+C^n- (1+j) + C^s=F = V C^s=r(V-F) and the answer.
(Quotation ..Shasoso.. C^n and C^p are also the same on. )
Frequently I am sorry.

Answer 4
That ..the donation... entire pension funds the cash that has been
entered this > There is no place to which it goes besides pension
funds.

Because do you turn around to F?
F indicates pension assets by abbreviating Fund. Cash is one of the properties.
It is not though it actually thinks the part that has it like cash to be making to the minimum and a transfer to other properties (debenture and stocks, etc.) because the amount of the total changes only because contents of F change.

>, a similar expression is to the question in the past of No.(2) of the test in 2005.
F at the time of of the end of fiscal year donates amount that in the under and the amount that falls below constant comparatively correspond to r with V as special insurance in pension system with > at the time end of next year.
Choose the count type where this > system shows F at the end of fiscal year when it is a stationary state/fiscal year V at the end.
It was, and > ..period Hatshara.. donating special insurance in ..assumed interest rate i.. yield on investment j however had the problem end of fiscal year >.
Does > be a stationary state and have PSL in this problem at the beginning of period?
The definition of the stationary state : though it must be V=F .
The limit equation of F and V had been approved just like the stationary state ..>.. why. >
= V and C^s=r(V-F) of (F+C^n- (1+j) + C^s=F (F+C^n- (1+i) It wrote in > and the answer.

It is interpreted that "Regularity" indicates no straw at the new year and the end of the year here the amount of the property (F) and the debt (V).
In a word, the situation of making the state that the amount of money of F and V doesn't change at the new year and the end of the year with it had the unredemption debt with F<V "Regularity" is indicated. Of course, it can be said, the situation setting of this problem is "Problem" in such a meaning in keeping leave the state of liabilities in excess of assets (F<V), and no permission in the management of pension funds of the reality, and another who thinks by giving a clear-cut attitude purely and mathematically doesn't think that it is when put out as a problem.

First of all, though F
(a)Standard insurance and the supply go in and out in the property at
the new year and F+C^n-B.
(
Because this is operated with (1+j), (F+C^n- (1+j).
Š
Because special insurance enters here, the property at the end of
fiscal year is (F+C^n- (1+j) + C^s.
(d)Because this is "Regularity" state, it becomes (F+C^n- (1+j)
+ C^s=F in unison with the property at the new year.
I think that it can similarly catch V.
(However, insurance is standard insurance and the idea interest rate
is an assumed interest rate. )

When you base the above
(F+C^n- (1+j) + C^s=F (V+C^n- (1+i) = V I think that it
becomes C^s=r(V-F).

Question 5
>> That ..>... donate the cash that has been entered to entire
pension funds thisThere is no place to which it goes besides pension
funds.

Because do you turn around to F?
...>.. F indicates pension assets by abbreviating Fund. Cash is one of the properties.
There is no > though actually thinks the part that has it like cash to be making to the minimum and a transfer to other properties (debenture and stocks, etc.) because the amount of the total changes only because contents of F change.

Is it good in understanding of in the company but pension funds' judging from the correspondences of two sentences, changing into other financial assets and having it?

Moreover, will it be a past service liability and be this an equal sign in the textbook from the content of the previous mail though it ..since P177 "Past service liability" of the word.. is not used and the word surplus is used by it?
( Word PSL is used in http://www.su-jine.net/ )

Moreover, so good a pin and not coming are the correspondences with the retirement benefit accounting though it is a matter of the other day's sort. The difference may (it but the projected benefit obligation and the not same) with the quotation of pension assets is recognized as a difference in the mathematical principle calculation of the unrecognition (henceforth mathematical principle difference) in Hi, pension assets are piled up, and it increases. (sort: Pension assets | mathematical principle difference)And, it will recognize from next year of or at this season as a minus of the retirement supply cost cost, and actual cash is not donated. (sort: Pension assets | mathematical principle difference)Moreover, pension assets, the mathematical principle difference, and the projected benefit obligation are done in the net and it sums it up as a retirement supply reserve on B/S.

The example was appended. (By the way, the mathematical principle
difference doesn't swell in the interest in Hi. )
http://f.hatena.ne.jp/actuary_math/20080819072806

The retirement benefit accounting and the corporate pension accounting are
that.
Please teach if you know.

Answer 5

Is it good in understanding of in the company but pension funds' judging from the correspondences of sentences of two >, changing into other financial assets and having it?

I think it is good in such understanding.


Will it be a past service liability and be this an equal sign in the textbook from > and the content of the previous mail though it ..since P177 "Past service liability" of the word.. is not used and the word surplus is used by it?>
(http://www.su-jine.net/)
So good a pin and not coming are the correspondences with the retirement benefit accounting though it is a matter of > and the other day's sorts. The difference may (it but the projected benefit obligation and the not same) with the quotation of pension assets is recognized as a difference in the mathematical principle calculation of the unrecognition (henceforth mathematical principle difference) in Hi, pension assets are piled up, and it increases. (sort: Pension assets | mathematical principle difference)And, it will recognize from next year of or at this season as a minus of the retirement supply cost cost, and actual cash is not donated. (sort: Pension assets | mathematical principle difference)Moreover, pension assets, the mathematical principle difference, and the projected benefit obligation are done in the net and it sums it up as a retirement supply reserve on B/S.

As for the amount where it had worked before when pension system began literally, the past service liability is to mean there is a difference between the liability reserve and pension assets, and it becomes "Debt" originally without insurance because it supplies it.
However," ..may similarly call by you, "Past service liability" by the difference of an assumed interest rate and an actual interest rate etc. because it is the same in the meaning that .."On the mathematical principle".. difference of the plus or minus amount between the liability reserve and pension assets after the system begins.. .."... (The reason made a past form is described later. )The distinction was not so done though it was occasionally called, "Late-started past service liability" when saying distinguishing this part.

However, the difference in the past service liability and the mathematical principle calculation is clearly distinguished by revising the accounting system in the retirement benefit accounting.
(For instance, Please see at
http://forums.xisto.com/no_longer_exists/
)

It will not catch up there because the book on the pension mathematical principle (In my understanding) has not changed having been revised in 1995 after that (It is after that as for the revision of the above-mentioned accounting system).
Moreover, I think that it takes the idea of consisting of it as a problem of the pension mathematical principle because it is caught as a difference between the liability reserve and both properties in the mathematical principle as possible to be being written even with above-mentioned URL.

Therefore, the problem of a pension mathematical principle present (actuary examination)
thinks whether I should link with the retirement benefit accounting and the corporate
pension accounting of the reality too much by giving a clear-cut attitude as the problem.


It is thought that neither the corporate pension accounting nor the
retirement benefit accounting are the distinguished one.
For instance,
http://forums.xisto.com/no_longer_exists/
Then,
It is an item "Corporate pension accounting/retirement benefit accounting".

Because I think that I become wrong perhaps if it digs more than this down about corporate pension accounting/retirement benefit accounting because it is unprofessional, could you pardon the respect?

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