IbnrClaims.jl
IbnrClaims.jl is a package that works with claim development triangles.
It calculates incurred but not reported claims reserves (IBNR).
Supports chain ladder and Bornhuetter-Ferguson methods.
Background
IbnrClaims.jl is a package that was born as an applied exercise of learning how to code, particularly in Julia. Since I have some actuarial background, it seemed natural to me to turn that knowledge into code.
The IbnrClaims.jl package does not pretend whatsoever to be a complete or extensive implementation of IBNR methods currently available.
Overview
- Works with incremental and cumulative claims triangles.
- Performs basic operations on triangles:
- Accumulates and deaccumulates claims.
- Calculates claims development factors (also known as loss development factors or LDF) of triangle columns.
- Calculates claims development quotas of triangle columns.
- Calculates the total IBNR reserve for a given triangle.
- Returns completed (known and estimated claims) claims triangles.
Usage
Creating a Triangle
Triangles are basically matrices that have the following restrictions:
- The number of rows and the number of columns have to be the same.
- Only zeros are allowed under the diagonal.
julia> using IbnrClaims
# creating an incremental triangle.
julia> ti = Incremental([23 15 18 11; 5 9 12 0; 7 8 0 0; 4 0 0 0])
Incremental Triangle {Int64}:
23 15 18 11
5 9 12 0
7 8 0 0
4 0 0 0
# creating an accumulated triangle.
julia> tc = Accumulated([23 38 56 67; 5 14 26 0; 7 15 0 0; 4 0 0 0])
Accumulated Triangle {Int64}:
23 38 56 67
5 14 26 0
7 15 0 0
4 0 0 0# obtaining the incurred claims of an accumulated triangle.
julia> incurred(tc)
4-element Vector{Any}:
67
26
15
4Basic Operations on Triangles
# deaccumulating an Accumulated Triangle.
julia> tdeacum(tc)
Incremental Triangle {Int64}:
23 15 18 11
5 9 12 0
7 8 0 0
4 0 0 0
# accumulating an Incremental Triangle
julia> taccum(tdc)
Accumulated Triangle {Int64}:
23 38 56 67
5 14 26 0
7 15 0 0
4 0 0 0
# calculating the claim development factors from an Accumulated Triangle.
julia> tfactors(tc)
4-element Vector{Float64}:
1.9142857142857144
1.5769230769230769
1.1964285714285714
1.0
# calculating the claim development factors from an Incremental Triangle.
# the method internally accumulates the triangle and calculates the factors of the Accumulated Triangle.
julia> tfactors(ti)
4-element Vector{Float64}:
1.9142857142857144
1.5769230769230769
1.1964285714285714
1.0# calculating the quotas for a given triangle.
julia> tquotas(tc)
4-element Vector{Float64}:
0.27688278664920757
0.5300327630141973
0.835820895522388
1.0
julia> tquotas(ti)
4-element Vector{Float64}:
0.27688278664920757
0.5300327630141973
0.835820895522388
1.0Chain Ladder
# calculating the IBNR reserve.
julia> ibnrcl(tc)
28.853826530612245
julia> ibnrcl(ti)
28.853826530612245# completing the original IBNR triangle with the Chain Ladder estimates.
julia> fillcl(tc)
Accumulated Completed Triangle {Float64}:
23.0 38.0 56.0 67.0
5.0 14.0 26.0 31.1071
7.0 15.0 23.6538 28.3001
4.0 7.65714 12.0747 14.4465
julia> fillcl(ti)
Incremental Completed Triangle {Float64}:
23.0 15.0 18.0 11.0
5.0 9.0 12.0 5.10714
7.0 8.0 8.65385 4.64629
4.0 3.65714 4.41758 2.37182Borhnuetter-Ferguson
Unlike the Chain Ladder methodology, Bornhuetter-Ferguson methodology requires additional information: primes and loss ratios.
julia> p = [80, 40, 30, 10];
julia> lr = [0.89, 0.74, 0.82, 0.6];
# calculating the IBNR reserve.
julia> ibnrbf(tc, p, lr)
20.759598802492818
julia> ibnrbf(ti, p, lr)
20.759598802492818# completing the original claims triangle with the Bornhuetter-Ferguson estimates.
julia> fillbf(tc, p, lr)
Accumulated Completed Triangle {Float64}:
23.0 38.0 56.0 67.0
5.0 14.0 26.0 30.8597
7.0 15.0 22.5224 26.5612
4.0 5.5189 7.35363 8.3387
julia> fillbf(ti, p, lr)
Incremental Completed Triangle {Float64}:
23.0 15.0 18.0 11.0
5.0 9.0 12.0 4.8597
7.0 8.0 7.52239 4.03881
4.0 1.5189 1.83473 0.985075