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Computes \(\mathrm{Var}(Z_x^{(m)}) = {}^{2}A_x^{(m)} - (A_x^{(m)})^2\).

Usage

var_Ax_m(x, i, m, model, ..., tol = 1e-12, j_max = 100000L)

Arguments

x

Age.

i

Effective annual interest rate.

m

Positive integer payment frequency.

model

Parametric survival model name.

...

Additional model parameters passed to survival-model functions.

tol

Numerical tolerance for truncating the infinite sum.

j_max

Maximum number of m-thly intervals in the sum.

Value

Numeric vector of variances.