Annuity-insurance relationships
annuity_relationships.RdIdentities linking annual and continuous annuity functions to the corresponding insurance functions.
Computes \(a_x = (v - A_x)/d\).
Computes \(\ddot{a}_x = (1 - A_x)/d\).
Computes \(\bar{a}_x = (1 - \bar{A}_x)/\delta\).
Computes \(a_{x:\overline{n}|} = (1 - A_{x:\overline{n}|})/d - 1 + {}_nE_x\).
Computes \(\ddot{a}_{x:\overline{n}|} = (1 - A_{x:\overline{n}|})/d\).
Computes \(\bar{a}_{x:\overline{n}|} = (1 - \bar{A}_{x:\overline{n}|})/\delta\).
Computes \({}_{n|}a_x = {}_nE_x a_{x+n}\).
Computes \({}_{n|}\ddot{a}_x = {}_nE_x \ddot{a}_{x+n}\).
Computes \({}_{n|}\bar{a}_x = {}_nE_x \bar{a}_{x+n}\).
Usage
annuity_identity_ax(x, i, model = NULL, ..., tbl = NULL)
annuity_identity_adotx(x, i, model = NULL, ..., tbl = NULL)
annuity_identity_abarx(x, i, model, ...)
annuity_identity_axn(x, n, i, model = NULL, ..., tbl = NULL)
annuity_identity_adotxn(x, n, i, model = NULL, ..., tbl = NULL)
annuity_identity_abarxn(x, n, i, model, ...)
annuity_identity_nax(
x,
n,
i,
model = NULL,
...,
tbl = NULL,
k_max = 5000,
tol = 1e-12
)
annuity_identity_nadotx(
x,
n,
i,
model = NULL,
...,
tbl = NULL,
k_max = 5000,
tol = 1e-12
)
annuity_identity_nabarx(x, n, i, model, ..., tol = 1e-10)Arguments
- x
Age.
- i
Effective annual interest rate.
- model
Optional survival model name.
- ...
Additional model parameters.
- tbl
Optional life table object for discrete identities.
- n
Term or deferral period in years.
- k_max
Maximum summation horizon for non-terminating models.
- tol
Truncation tolerance for non-terminating models.