Monte Carlo simulation of a life insurance

Simulates present values of a discrete single-life insurance payable at the end of the year of death, or at maturity for an endowment insurance. Monetary values retain the original log interest rate, even when the displayed annual effective rate loses range. Finite-horizon survivors are censored: Kx = n is a placeholder and died_within_horizon = FALSE, not an observed death at that duration.

Usage

simulate_insurance_x(
  lt,
  x = NULL,
  i = NULL,
  i_type = NULL,
  m = NULL,
  type = c("whole", "term", "endowment"),
  n = Inf,
  benefit = 1,
  method = c("inverse"),
  n_sim = 10000L,
  seed = NULL,
  output = c("simulations", "summary"),
  ...
)

Arguments

lt

A life table or a tidyact_life_contract.

x

Integer actuarial age.

i

Numeric scalar interest-rate input.

i_type

Interest-rate convention.

m

Positive integer nominal conversion frequency.

type

"whole", "term", or "endowment".

n

Positive integer term, or Inf for whole life.

benefit

Nonnegative insurance benefit.

method

Simulation method. Currently only "inverse".

n_sim

Positive integer number of simulations.

seed

Optional nonnegative integer seed.

output

"simulations" or "summary".

...

Transitional compatibility for mortality_table, age, rate, rate_type, insurance_type, and term_years.

Value

A tibble with one row per simulation, or a summary. Simulation output includes benefit_indicator, benefit_time, present_value, and pv_benefit.

See also

Other simulation: simulate_annuity_x()

Other life-contingencies: add_insurance(), add_premium_schedule(), annuity_multi(), annuity_x(), annuity_xy(), insurance_variable_k(), insurance_x(), insurance_xy(), life_contract(), premium_gross(), premium_x(), premium_xy(), reserve_x(), reserve_xy(), simulate_annuity_x()

Examples

lt <- data.frame(
  x = 60:66,
  lx = c(100000, 99000, 97500, 95500, 93000, 90000, 0)
)

simulate_insurance_x(
  lt = lt,
  x = 60,
  i = 0.05,
  type = "term",
  n = 5,
  benefit = 100000,
  n_sim = 25,
  seed = 123
)
#> # A tibble: 25 × 26
#>    sim_id simulation_id contract_type      x   age     n term_years type 
#>     <int>         <int> <chr>          <int> <int> <int>      <int> <chr>
#>  1      1             1 term_insurance    60    60     5          5 term 
#>  2      2             2 term_insurance    60    60     5          5 term 
#>  3      3             3 term_insurance    60    60     5          5 term 
#>  4      4             4 term_insurance    60    60     5          5 term 
#>  5      5             5 term_insurance    60    60     5          5 term 
#>  6      6             6 term_insurance    60    60     5          5 term 
#>  7      7             7 term_insurance    60    60     5          5 term 
#>  8      8             8 term_insurance    60    60     5          5 term 
#>  9      9             9 term_insurance    60    60     5          5 term 
#> 10     10            10 term_insurance    60    60     5          5 term 
#> # ℹ 15 more rows
#> # ℹ 18 more variables: insurance_type <chr>, benefit <dbl>, i <dbl>,
#> #   rate <dbl>, i_type <chr>, rate_type <chr>, m <int>, i_effective <dbl>,
#> #   Kx <int>, curtate_lifetime <int>, death_age <dbl>,
#> #   died_within_horizon <lgl>, covered <lgl>, benefit_indicator <dbl>,
#> #   payment_time <dbl>, benefit_time <dbl>, present_value <dbl>,
#> #   pv_benefit <dbl>