An illustrative dataset---a matrix (of the dimensions 10x10) with ten
completed years of claims payment developments of the Midwest Family Mutual
Insurance company from the period 1988 -- 1997. The data matrix contains ten
origin/occurrence years (with the first row representing the incident year
1988) and ten consecutive development periods/years (in columns).
data(MidwestMutual)
A simple 10x10 matrix of a class triangle with ten origin years
(rows) each being fully developed within ten consecutive development
periods/years (columns)
matrix rows with the occurrence year (origin)
matrix columns with the development period (development)
The run-off triangle (the upper-left triangular part of the data matrix) contains only positive increments making the triangle suitable for the standard modelling approach---the over-dispersed Poisson model (GLM approach).
In practice, the run-off triangle only (the upper triangular part) of the data matrix is known while the bottom-right triangular part is treated as a future outcome (an "unknown" truth) that should be estimated/predicted. The Midwest Family Mutual Insurance data matrix is fully observed to allow for some retrospective goodness-of-fit evaluations.
Meyers, G. G. and P. Shi (2011). Loss reserving data pulled from NAIC Schedule P. Available from https://www.casact.org/publications-research/research/research-resources
Maciak, M., Mizera, I., and Pešta, M. (2022). Functional Profile Techniques for Claims Reserving. ASTIN Bulletin, 52(2), 449-482. DOI:10.1017/asb.2022.4 (Portfolio #2)