COMPARISON FOR ESTIMATION RISK OF O/S AND
IBNR RESERVE USING THE CHAIN LADDER METHOD,
THE CREDIBILITY MODEL AND MCMC METHODS
Gi Wook Bae
LG Insurance, Commercial Actuarial Team, Seoul, Korea
Abstract. The simulations and comparisons between credibility models and several
MCMC methods show that the fully Bayesian approach using MCMC method
produce a smaller estimation errors and the ratio of standard error to estimated
reserves than that of credibility model, which lead good results for the estimated
reserves.
1. Introduction
For MCMC (Markov Chain Mote Carlao) simulations, the simple accessibility and
wide applicability of the sampling based approach to Bayesian inference suggests
the feasibility of a common purpose software for Bayesian analysis. Up to this view
point, the user simply writes a short lines Gibbs or Metropolis-Hastings sampler
code for the problem at hand, and modifies it to fit whatever subsequent problems
come along. Users have also used that some high-standard languages (S-Plus,
XLISP-STAT) which are convenient for the data entry, graphical convergence
monitoring, and posterior summary statistics, while lower-level compiled
languages(C or Fortran) are needed to facilitate the enormous amount of random
generation and looping in the sampling procedure.
The lower-level language is the more difficult one, since the computer has to be
coded to understand a statistical model, or the prior and likelihood components,
and make the necessary sampling distributions before sampling. These problems
to overcome, a program has been developed and available via internet as freeware,
i.e. BUGS (Bayesian inference Using Gibbs Sampling). This program is written by
S-Plus-like syntax for specifying hierarchical model and developed by MRC
Biostatistics Unit at the University of Cambridge.
The program determines the full conditional distributions necessary for the Gibbs
sampler and the non-explicit conditional distributions for the Metropolis-Hastings
sampler by conv