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Multi-life pure endowments

multilife_pure_endowments.Rd

Computes pure endowment actuarial present values for joint-life and last-survivor statuses for two independent lives.

Usage

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

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

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.

Value

A numeric vector of actuarial present values.

Details

nExy() computes an \(n\)-year joint-life pure endowment, payable at time \(n\) if both lives survive.

nExybar() computes an \(n\)-year last-survivor pure endowment, payable at time \(n\) if at least one life survives.

The joint-life pure endowment is $$ {}_nE_{xy} = v^n\,{}_np_{xy}. $$

The last-survivor pure endowment is $$ {}_nE_{\overline{xy}} = v^n\,{}_np_{\overline{xy}}. $$

Under independence, $$ {}_np_{xy} = {}_np_x\,{}_np_y $$ and $$ {}_np_{\overline{xy}} = {}_np_x + {}_np_y - {}_np_x\,{}_np_y. $$

Examples

nExy(
  x = 40,
  y = 50,
  n = 10,
  i = 0.05,
  model = "uniform",
  omega = 100
)
#> [1] 0.4092755

nExybar(
  x = 40,
  y = 50,
  n = 10,
  i = 0.05,
  model = "uniform",
  omega = 100
)
#> [1] 0.5934495