life_modeling_problem.md

library(data.table)

q <- c(0.001,
       0.002,
       0.003,
       0.003,
       0.004,
       0.004,
       0.005,
       0.007,
       0.009,
       0.011)

w <- c(0.05,
       0.07,
       0.08,
       0.10,
       0.14,
       0.20,
       0.20,
       0.20,
       0.10,
       0.04)

P <- 100
S <- 25000
r <- 0.02

dt <- as.data.table(cbind(q,w))

npv <- function(cf, r, S, P) {
  cf[, inforce := shift(cumprod(1 - q - w), fill = 1)
  ][, lapses := inforce * w
  ][, deaths := inforce * q
  ][, claims := deaths * S
  ][, premiums := inforce * P
  ][, ncf := premiums - claims
  ][, d := (1/(1+r))^(.I)
  ][, sum(ncf*d)]
}

npv(dt,r,S,P)
#> [1] 50.32483

microbenchmark::microbenchmark(npv(dt,r,S,P))
#> Unit: milliseconds
#>              expr    min      lq     mean  median      uq    max neval
#>  npv(dt, r, S, P) 2.5791 2.71035 2.964293 2.85625 3.10385 6.0357   100

^{Created on 2021-01-15 by the reprex package (v0.3.0)}

Updated Rankings for the "Life Modeling Problem":

code	algorithm	relative	absolute timing (mean)
Julia	accumulating for loop	1x	135 nanoseconds
Rust	accumulating for loop	3x	360 nanoseconds
Julia	vector	4x	500 nanoseconds
Python numpy	vector	155x	21 microseconds
R vectorized	vector	520x	70 microseconds
R data.table	data.table vector	22000x	3 milliseconds