mage67 (mage67) wrote,
mage67
mage67

  • Mood:

My algorithm

I worked so hard this morning on a premium scheme for an insurance product I worked on that will probably never be used. It prevents the insured from overpaying his premium. Many times his savings according to this scheme and the policy I worked on can easily be over $1 million.

However I doubt the company I work for has an interest in preventing the insured from overpaying when he doesn't have to.

If you don't like algorithms, for god's sake don't



If the premium solve is under $100,000, then we
bump up the premiums to the minimums allowed by the policy by the following
algorithm. 


 


Let intendedPremiumt = The
premium scheduled to be paid in policy year t


Let illustratedPremiumt =
The premium illustrated to be paid in policy year t


Let intendedTotPremt
= The Sum of Premiums and 1035 Rollover Premiums intended to be paid from
policy issue up to and including policy year t


Let illustratedTotPremt
= The Sum of Premiums and 1035 Rollover Premiums illustrated as to be paid from
policy issue up to and including policy year t


Let differenceTotPremt = illustratedTotPremt
- intendedTotPremt


 


illustratedPremium1
= maximum ($250,000 , Target Premium) in all cases


 


If a premium is
to be paid in year t, and differenceTotPremtintendedPremiumt
then force illustratedPremiumt = 0.


 


If a premium is
to be paid in year t and differenceTotPremt < intendedPremium
and intendedPremiumt < $100,000 then force illustratedPremiumt
= $100,000.


 


 


An additional fix for accuracy can be added as
follows:


 


If intendedPremiumt
> $100,000 and differenceTotPremt >0, then force

illustratedPremiumt = maximum($100,000 , (intendedPremiumt
- differenceTotPremt))


 


Instead of making the adjustments based on
Premium schedules, actuarial may decide to base the adjustments on Cash
Values.  I could suggest a way to deal
with that if anyone is curious.


 


The solves I just suggest just on Premium
Schedules should be sufficient though if they can be agreed upon.


 





Example1:


If the premium solve becomes $75,000 and
$100,000 is paid instead for a 50 year old insured,
then $25,000 is overpaid every year. 
After 4 years of this, ideally the next premium should not be paid.


 


Example 2:


If the premium solve is $60,000 in the first 8
years and the premium becomes $125,000 for policy years 9 through 20 for a 50
year old insured, then the premium schedule will be as adjusted below


 



Policy Year



illustratedPremium



intendedPremium



illustratedTotPrem



intendedTotPrem



1



$250,000



$60,000



$250,000



$60,000



2



$0



$60,000



$250,000



$120,000



3



$0



$60,000



$250,000



$180,000



4



$0



$60,000



$250,000



$240,000



5



$100,000



$60,000



$350,000



$300,000



6



$100,000



$60,000



$450,000



$360,000



7



$0



$60,000



$450,000



$420,000



8



$100,000



$60,000



$550,000



$480,000



9



$100,000



$125,000



$650,000



$605,000



10



$100,000



$125,000



$750,000



$730,000



11



$105,000



$125,000



$855,000



$855,000



12



$125,000



$125,000



$980,000



$980,000



13



$125,000



$125,000



$1,105,000



$1,105,000



14



$125,000



$125,000



$1,230,000



$1,230,000



15



$125,000



$125,000



$1,355,000



$1,355,000



16



$125,000



$125,000



$1,480,000



$1,480,000



17



$125,000



$125,000



$1,605,000



$1,605,000



18



$125,000



$125,000



$1,730,000



$1,730,000



19



$125,000



$125,000



$1,855,000



$1,855,000



20



$125,000



$125,000



$1,980,000



$1,980,000




 



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