ADONGO’S TARGET BALANCE EQUATIONS
Today I am
most glad to continue from my previous Diary(or Weblog) titled, “Adongo’s
Minimum Uncertainty Method”.
In life
insurance and theory of employment, interest and money, cash is needed to
satisfy the transactions motive, the need to pay benefits. The disbursement of
cash includes the payment of wages and salaries, trade-debts, death benefits
and retirement benefits. The cash inflows(or premium) must be synchronized, if
not perfectly, nearly. The equality between the inflows(or premiums) and
outflows(benefits) is to determine the company target-fund balance.
The target-
fund balance involves a trade-off between the benefits of holding too much cash
and premiums of holding too much benefits.
Consider a
discrete whole life policy purchase each of the lx lifes for an annual premium.
If lx+k survive at years x+k and dx+k death between x+k
and x+k+1. At an effective annual rate of interest r, the net annual premiums is;
NAPx*lx+C*NAPx*lx+1
+C2*NAPx*lx+2 +...=Cdx+C2dx+1
+C3dx+2 +......
Or
NAPx +C*NAPx+C2*NAPx
+....=C/qx +C2/qx+1 +C3/qx+2
+.....
For each
i=1,2,3,.....k
Where;
NAPx=net annual premium at age x.
Lx+k=lifes purchase at age x+k.
C=Claims(or benefits)
dx+k=death at age x+k.
FUND BALANCE
In Adongo’s(or my) target- balance equations,
aggregate fund of balance to which benefits are withdrawn and which earns interest
rate r, at the end of kth year policy. The balance of the fund is;
Bf=∑lx+kNAPx - ∑Cx+k
The net
premiums are exactly sufficient to cover the benefits if only the balance of the
fund at the end of the kth
year is zero(0).
REFERENCE
*Adongo's Ayine William(me), Diary(or weblog), "Adongo's Minimum Uncertainty Method"
