Four BASIC programs for life contingencies

[Richard Purvey]

BASIC Programs For Four Of The Standard Algorithmic Calculations Currently Included In The Actuarial Life Contingencies Syllabus

 

In each case, make the first line of the program:

 

10 DEF FNS(U)=whatever the survival function, S(U), is.

 

For example, for a Makeham with A equal to 0.00022, B equal to 2.7*10^(-6) and c equal to 1.124, make the first line of the program:

 

10 DEF FNS(U)=EXP(-0.00022*U-2.7*10^(-6)*(1.124^U-1)/LN(1.124))

 

And then;

 

If you want the program to calculate an n-year temporary curtate life expectancy for (x) when executed then add on the following:

 

20 INPUT x,n

 

30 ANSWER=0

 

40 FOR r=1 TO n

 

50 ANSWER=ANSWER+FNS(x+r)

 

60 NEXT r

 

70 ANSWER=ANSWER/FNS(x)

 

80 PRINT ANSWER

 

90 END

 

Or if you want the program to calculate the actuarial present value of an n-year temporary immediate life annuity, with a discount factor of v, of 1 per year payable m times per year for (x) (m may be equal to 1) when executed then add on the following:

 

20 INPUT x,n,m,v

 

30 ANSWER=0

 

40 FOR r=1 TO m*n

 

50 ANSWER=ANSWER+v^(r/m)*FNS(x+r/m)

 

60 NEXT r

 

70 ANSWER=ANSWER/(m*FNS(x))

 

80 PRINT ANSWER

 

90 END

 

Or if you want the program to calculate the actuarial present value of an n-year temporary life annuity due, with a discount factor of v, of 1 per year payable m times per year for (x) (m may be equal to 1) when executed then add on the following:

 

20 INPUT x,n,m,v

 

30 ANSWER=0

 

40 FOR r=0 TO m*n-1

 

50 ANSWER=ANSWER+v^(r/m)*FNS(x+r/m)

 

60 NEXT r

 

70 ANSWER=ANSWER/(m*FNS(x))

 

80 PRINT ANSWER

 

90 END

 

Or if you want the program to calculate the actuarial present value of a death benefit, with a discount factor of v, of 1 payable at the end of the 1/m year of death for (x) (m may be equal to 1), provided this occurs within n years, when executed then add on the following:

 

20 INPUT x,n,m,v

 

30 ANSWER=0

 

40 FOR r=0 TO m*n-1

 

50 ANSWER=ANSWER+v^(r/m)*FNS(x+r/m)

 

60 NEXT r

 

70 ANSWER=ANSWER/(m*FNS(x))

 

80 ANSWER=1-v^n*FNS(x+n)/FNS(x)-m*(1-v^(1/m))*ANSWER

 

90 PRINT ANSWER

 

100 END

 

 

I have written the above programs in BBC BASIC which is very similar to the more commonly used VB.

[Author]

Posts