Provides tidyverse-aligned tools for actuarial mathematics and life contingencies, including life tables, survival probabilities, actuarial present values of cash flows, life annuities, life insurance, premiums, reserves, multiple-life calculations, Monte Carlo simulation, collective risk models, insurance coverage, tail risk measures, and deterministic cash-flow diagrams. The package emphasizes clear actuarial notation, reproducible workflows, and pipe-friendly tools for actuarial education and applied actuarial analysis.
Actuarial mathematics in R with transparent formulas, reproducible workflows, and tidy outputs where they add value.
tidyactuarial provides tools for financial mathematics, life contingencies, and collective risk in R. The package is designed so that the actuarial model remains visible: formulas, timing conventions, mortality assumptions, and valuation dates come first; computation is then used to reproduce, audit, and scale the calculation.
This repository contains the 0.2.0 release candidate. This README describes that candidate; it does not imply that CRAN has accepted or published it. Until then, installation from CRAN may provide an earlier release without some of the features and corrections described here.
Install the stable version from CRAN:
install.packages("tidyactuarial")
Load the package with:
library(tidyactuarial)
The package currently includes tools for:
The full API is organized by actuarial area in the Reference section of the package website.
The package does not try to replace actuarial reasoning with software.
For a payment of amount $C$ at time $t$, financial valuation begins with
$$ PV = C(1+i)^{-t}. $$
For a payment contingent on survival of a life aged $x$, the corresponding actuarial structure becomes
v^t,{}_tp_x. $$
tidyactuarial keeps these quantities explicit and then provides functions that make the same calculations easier to reproduce across scenarios, portfolios, contracts, and datasets.
Different rate conventions can first be placed on a common annual-effective basis.
library(tidyactuarial)
library(dplyr)
library(tibble)
rates <- tibble(
product = c(
"effective",
"nominal interest",
"force",
"nominal discount"
),
i = c(
0.0620,
0.0605,
0.0605,
0.0590
),
i_type = c(
"effective",
"nominal_interest",
"force",
"nominal_discount"
),
m = c(
1,
12,
1,
4
)
)
rates |>
mutate(
i_effective = standardize_interest(
i_type = i_type,
i = i,
m = m
),
value_6y = future_value(
C = 25000,
i = i_effective,
t = 6
)
)
This pattern is useful when actuarial assumptions arrive in heterogeneous forms but the valuation model requires a common basis.
For a loan balance $B_{t-1}$, interest $I_t$, scheduled payment $R_t$, and extra principal $E_t$,
E_t. $$
A standard amortization schedule can be generated directly:
amort_schedule(
principal = 50000,
n = 5,
i = 0.12,
i_type = "nominal_interest",
m = 12,
k = 12
)
When rates or payment rules vary over time, amort_schedule_general() provides the more flexible engine.
principal <- 120000
rates <- c(
0.04,
0.05,
0.06,
0.07,
0.08,
0.09
)
amort_schedule_general(
principal = principal,
n = 6,
i = rates,
payment = NULL
)
price <- bond_price(
face = 1000,
c = 0.05,
n = 10,
k = 2,
y = 0.06,
y_type = "effective"
)
duration <- bond_duration(
face = 1000,
c = 0.05,
n = 10,
k = 2,
y = 0.06,
y_type = "effective"
)
convexity <- bond_convexity(
face = 1000,
c = 0.05,
n = 10,
k = 2,
y = 0.06,
y_type = "effective"
)
tibble(
price = price,
duration = duration,
convexity = convexity
)
The package uses the same actuarial specification to move from bond price to duration and convexity.
data("soa08lt")
premium_x(
lt = soa08lt,
x = 40,
i = 0.05,
type = "term",
benefit = 100000,
n = 20,
k = 12,
n_prem = 10,
output = "summary"
)
The same contract can be assembled progressively:
soa08lt |>
life_contract(
lives = "single",
x = 40,
i = 0.05
) |>
add_insurance(
type = "term",
benefit = 100000,
n = 20
) |>
add_premium_schedule(
k = 12,
n_prem = 10,
timing = "due"
) |>
premium_x(
output = "summary"
)
The pipe records the actuarial construction of the contract; it does not replace the underlying equation of equivalence.
Four introductory articles develop complete workflows rather than isolated function calls:
They are available from the Articles menu of the package website.
Not every actuarial result needs to be a tibble.
tidyactuarial uses several output patterns depending on the task:
This keeps simple calculations simple while allowing larger analyses to remain inspectable and reproducible.
The package is developed with automated unit and regression tests. Continuous integration is configured for Linux, Windows, and macOS, including the declared minimum R version on Ubuntu. A successful run applies to the commit it checks; it does not certify later development changes.
For released work where stability is the priority, use the CRAN version.
Function-level documentation is available from R:
help(package = "tidyactuarial")
?standardize_interest
?amort_schedule_general
?bond_price
?annuity_x
?premium_x
?reserve_x
The package website provides:
Bug reports and reproducible examples are welcome through the project issue tracker.
For numerical issues, include whenever possible:
sessionInfo().The package follows standard actuarial and financial mathematics. Useful background references include:
MIT License. See LICENSE for details.