Details and Options
ResourceFunction["ActuarialCommutation"] functions can be used to compute a number of quantities of interest in actuarial mathematics, such as the value of an annuity or death benefit.
The parameter l is a list containing the fraction of the initial population surviving at the start of each time unit.
The parameter v is a discount rate generally between 0 and 1, showing the value of money received one year from now.
The "ReturnForm" option directs the form in which the data is returned: permissible option values are as follows:
"FunctionAssociation" returns an association in which the commutation function names are the keys and the values are the values of each function at each successive unit of time;
"TimeAssociation" returns a nested association in which the outer keys are the successive units of time and the values are associations in which the keys are the names of the commutation functions and the values are the value of that function at the specified unit of time.
"FunctionValues" returns a nested list in which each outer list represents the values of a commutation function at a successive unit of time. The lists are ordered as "D", "N", "S", "C", "M", "R". For example, the fourth element of the returned values contains a list of the values for the "C" commutation function.
“TimeValues” returns a nested list in which each outer list represents a unit of time. Each inner list contains six values, one for each of the six commutation functions and in the order "D", "N", "S", "C", "M", "R".
The "InitialTime" option can (and probably should) be used when the mortality table begins at an age other than 0.
Although commutation functions and tables displaying them are used less frequently than in times when computation was less accessible, they are still a useful tool in swiftly computing quanities of interest in actuarial mathematics.