lifeinsurance.ijs

Script: ~addons/finance/finexec/actuariallife/lifeinsurance.ijs
Contributor: William Szuch
Updated: 2022 6 25
Depend: ~addons/finance/fp/qxtables/qxtables/qxtools.ijs’
Definitions: loaded to locale base
Status: Review
Script scource: lifeinsurance.ijs
Definitions to calculate life issurance factors for
single and multiple lives.
Qx tables loaded to the locale base
See: Qx_ALL for a list of names.
See: Qx_ALT for a list of Australian Life Tables.
All mortality tables start at age = 0.
(1) Extending Qx tables by 5 years.

(2) Multiple lives

(3) Variable interest rates

Equations:
NF

Definitions

A asx, asx_M, asxn, asxn1

asx (dyad)

Form: tacit
Calculate the value of a whole of life issurance for
a sum insured of one payable at the end of the year death.
syntax:
(Qx;E)asx(Age)
Qx = name of Qx table starting at age = 0
E = yearly effective interest rate
Age = integer ages

Example

   (AL_49_52_M_ULT;0.05)asx(20)
0.0966624
   (AL_49_52_M_ULT;0.05)asx(20 40 60 80)
0.0966624 0.222605 0.472562 0.756022

asx_M (monad)

Form: tacit
Monadic form of asx.
Calculate the value of a whole of life issurance for
a sum insured of one payable at the end of the year death.

Syntax

asx_M(Qx;Age;E)
Qx = name of Qx table starting at age = 0
Age = integer ages
E = yearly effective interest rate

Example

   asx_M(AL_AM92_ULT;17;0.04)
0.10127
    asx_M(AL_AM92_ULT;17 50 60 65;0.04)
0.10127 0.329072 0.456402 0.527864

asxn (dyad)

Form: explicit
Same as asxn1 but allow multiple lives and terms.
Calculate the value of a term life issurance for
a sum insured of one payable at the end of the year death.
syntax:
(Qx;E)asxn(Age;N)
Qx = name of Qx table starting at age = 0
E = yearly effective interest rate
Age = integer ages
N = term of insurance - integer years

Example

   (AL_49_52_M_ULT;0.05)asxn(20;40)
0.0394944
   (AL_AM92_ULT;0.05)asxn(20 40;20)
0.00762835 0.0304109
   (AL_AM92_ULT;0.05)asxn(20;20 30 40)
0.00762835 0.0116736 0.0189453
   (AL_AM92_ULT;0.05)asxn(20 40;20 30 40)
0.00762835 0.0116736 0.0189453
 0.0304109 0.0654055   0.11467

asxn1 (dyad)

Form: tacit
Calculate the value of a term life issurance for
a sum insured of one payable at the end of the year death.
(one life)
syntax:
(Qx;E)asx(Age;N)
Qx = name of Qx table starting at age = 0
E = yearly effective interest rate
Age = integer ages
N = term of insurance - integer years

Example

   (AL_49_52_M_ULT;0.05)asxn1(40;20)
0.0671175
   (AL_49_52_M_ULT;0.05)asxn1(20;40)
0.0394944