Method Deterministic compartmental models are explored as extensible tools to describe and project the insurance claims process using a small number of parameters, including measure of case reserve robustness. A Schedule-P reserving case study illustrates the application of a nonlinear hierarchical (“mixed-effects”) framework to fit compartmental models too outstanding and cumulative paid claims development triangles, simultaneously. This allows one or more of the claims process parameters to vary by claims cohort in accordance with a statistical distribution. An optional Bayesian implementation facilitates the robust incorporation of external information and judgment into the projection of reserve uncertainty.
Results A flexible stochastic reserving framework is established, with benefits including the ability to explicitly account for reporting and/or settlement rate changes, make inferences about components of the claims process and scenario test future process changes using information gathered across the business.
Conclusions Hierarchical compartmental models can describe and project the insurance claims process in an optional level of detail for the purpose of setting reserves.
Availability Frequentist model R code is contained in Appendix E, Bayesian model OpenBUGS code is contained in Appendix F and an illustration spreadsheet is available at: http://www.casact.org/pubs/forum/16sforum/.
Keywords Stochastic loss reserving, compartmental reserving models, claims process modeling, hierarchical models, nonlinear mixed-effects, Bayesian modeling, MCMC
