Joint-life annuities — joint_life

Computes temporary and whole-life joint-life annuities-due and annuities-immediate for two independent lives.

Usage

adotxyn(x, y, n, i, tbl = NULL, model = NULL, ...)

axyn(x, y, n, i, tbl = NULL, model = NULL, ...)

adotxy(x, y, i, tbl = NULL, model = NULL, ..., k_max = 5000L, tol = 1e-12)

axy(x, y, i, tbl = NULL, model = NULL, ..., k_max = 5000L, tol = 1e-12)

Arguments

x: Age of the first life. May be scalar or vector.
y: Age of the second life. May be scalar or vector.
n: Nonnegative integer term. May be scalar or vector.
i: Effective annual interest rate. May be scalar or vector.
tbl: Optional life table object.
model: Optional parametric survival model.
...: Additional parameters passed to the survival model.
k_max: Maximum summation horizon used for non-terminating parametric survival models.
tol: Positive convergence tolerance for whole-life summations.

Value

A numeric vector of annuity actuarial present values.

Details

adotxyn() computes an $n$-year temporary joint-life annuity-due.

axyn() computes an $n$-year temporary joint-life annuity-immediate.

adotxy() computes a whole-life joint-life annuity-due.

axy() computes a whole-life joint-life annuity-immediate.

All calculations assume independence between the two future lifetimes.

The temporary annuity-due is $$ \ddot{a}_{xy:\overline{n}|} = \sum_{k=0}^{n-1} v^k\,{}_kp_{xy}. $$

The temporary annuity-immediate is $$ a_{xy:\overline{n}|} = \sum_{k=1}^{n} v^k\,{}_kp_{xy}. $$

For life-table calculations, the whole-life sums terminate at the last duration supported jointly by the two lives. For parametric models, the sums are evaluated until convergence or until k_max is reached.

Examples

adotxyn(
  x = 40,
  y = 50,
  n = 10,
  i = 0.05,
  model = "uniform",
  omega = 100
)
#> [1] 6.956659

axyn(
  x = 40,
  y = 50,
  n = 10,
  i = 0.05,
  model = "uniform",
  omega = 100
)
#> [1] 6.365935

adotxy(
  x = 40,
  y = 50,
  i = 0.05,
  model = "uniform",
  omega = 100
)
#> [1] 10.96154

axy(
  x = 40,
  y = 50,
  i = 0.05,
  model = "uniform",
  omega = 100
)
#> [1] 9.961536