Handling Sparse Data for Reserving Using Bayesian MCMC

A sparse data set may consist of either a limited number of exposures (a small number of policyholders), a limited number of accident years or a combination of both. This paper will demonstrate, through a series of reserve modeling examples that will focus on displaying the results using graphs, how the Bayesian MCMC (Markov Chain Monte Carlo) modeling environment can assist an actuary in providing plausible reserve estimates to a client, even with sparse data.Actuaries have dealt with the issue of limited data in practice by applying credibility weighting. Bayesian MCMC offers the means to incorporate a form of credibility weighting in a regression type model and this paper will provide examples that show how that combination can be used to model reserve estimates given sparse data.The theory behind Bayesian MCMC, as well as background on how STAN (the software used in the paper to run Bayesian MCMC models) operates, can be found in textbooks and articles cited in the bibliography. Explaining the theory underlying Bayesian MCMC is outside the scope of this paper. The code used to create the reserve modeling examples is available via a Rmarkdown file. Instructions on required software installation are included.