| Title: | Insurance Reserve Calculations |
| Version: | 0.1.0 |
| Description: | Calculates insurance reserves and equivalence premiums using advanced numerical methods, including the Runge-Kutta algorithm and product integrals for transition probabilities. This package is useful for actuarial analyses and life insurance modeling, facilitating accurate financial projections. |
| License: | GPL-3 |
| Encoding: | UTF-8 |
| Imports: | Rcpp, RcppArmadillo |
| LinkingTo: | Rcpp, RcppArmadillo |
| NeedsCompilation: | yes |
| RoxygenNote: | 7.3.2 |
| Suggests: | knitr, rmarkdown, testthat (≥ 3.0.0) |
| VignetteBuilder: | knitr |
| Config/testthat/edition: | 3 |
| Packaged: | 2025-02-28 21:59:24 UTC; Oskar |
| Author: | Oskar Allerslev [aut, cre] |
| Maintainer: | Oskar Allerslev <Oskar.m1660@gmail.com> |
| Repository: | CRAN |
| Date/Publication: | 2025-02-28 22:10:02 UTC |
Equivalence Premium
Description
This function calculates the equivalence premium for an insurance contract.
Usage
equiv_premium(s, t, Lambda, R, dR, mu, r, n)
Arguments
s |
Initial timepoint |
t |
End timepoint |
Lambda |
Intensity matrix |
R |
Reward matrix |
dR |
Differential of reward matrix |
mu |
Equivalence premium guess |
r |
Constant rate as a scalar |
n |
Number of steps for the Runge-Kutta algorithm |
Value
A scalar
Examples
Lambda <- function(x) matrix(c(-0.1, 0.1, 0.05, -0.05), nrow = 2)
R <- function(x, mu) matrix(c(mu, 0, 0, mu), nrow = 2) # Corrected
dR <- function(x, mu) matrix(c(0.1, 0, 0, 0.1), nrow = 2)
equiv_premium(0, 80, Lambda, R, dR, 0.05, 0.03, 100)
Productintegral (C++ optim)
Description
This function calculates the product integral of a matrix function from s to t. It uses a Runge-Kutta method implemented in C++ for efficiency.
Usage
prodint(A, s, t, n)
Arguments
A |
A function returning a matrix (intensity matrix) |
s |
Initial timepoint |
t |
End timepoint |
n |
Number of steps for the Runge-Kutta algorithm |
Value
A matrix (transition probabilities if A is an intensity matrix)
Reserve This function calculates the reserve given the reward matrix and some constant rate This function requires proper construction of reward matrix as specified in the lecture notes provided in the course Liv1 at the University of Copenhagen.
Description
Reserve This function calculates the reserve given the reward matrix and some constant rate This function requires proper construction of reward matrix as specified in the lecture notes provided in the course Liv1 at the University of Copenhagen.
Usage
reserve(t, TT, Lambda, R, mu, r, n)
Arguments
t |
initial timepoint |
TT |
end timepoint |
Lambda |
intensity matrix |
R |
reward matrix |
mu |
equivalence premium |
r |
constant rate as a scalar |
n |
number of steps for the Runge-Kutta algorithm |
Value
Returns a matrix of statewise reserves
Examples
Lambda <- function(x) matrix(c(-0.1, 0.1, 0, -0.1), 2, 2)
R <- function(x, mu) matrix(c(0, 0, 0, mu), 2, 2)
reserve(0, 80, Lambda, R, 200000, 0.01, 1000)
Reserve with Dynamic Rate
Description
This function calculates the reserve matrix using a dynamic interest rate function.
It extends the functionality of the reserve function by allowing the rate to vary over time.
Usage
sreserve(t, TT, Lambda, R, mu, r, n)
Arguments
t |
Initial timepoint |
TT |
End timepoint |
Lambda |
Intensity matrix |
R |
Reward matrix |
mu |
Equivalence premium |
r |
A function of time that returns the interest rate |
n |
Number of steps for the Runge-Kutta algorithm |
Value
A matrix representing statewise reserves
Examples
Lambda <- function(x) matrix(c(-0.1, 0.1, 0, -0.1), 2, 2)
R <- function(x, mu) matrix(c(0, 0, 0, mu), 2, 2)
rentefun <- function(x) { 0.01 + 0.001 * x } # Dynamic interest rate
sreserve(0, 80, Lambda, R, 200000, rentefun, 1000)