Verrall: predictive distribution for reserves which incorporate expert opinion

Introduction

Key definitions

C incremental losses

D cumulative losses

One important property of Bayesian methods that makes them suitable for use with a stochastic reserving model is that they allow us to incorporate expert knowledge in a natural way

The basic idea behind MCMC methods is to simulate the posterior distribution by breaking the simulation process down into a number of simulations that are as easy to carry out as possible.

Instead of trying to simulate all the parameters at once, MCMC methods use the conditional distribution of each parameter, given all the others. In this way, the simulation is reduced to a univariate distribution, which is much easier to deal with.

In general, when selecting prior distributions, the variance assigned to the distribution dictates how the model will fit to the data

Higher variances give less credibility to the prior mean set, meaning that the distribution will ultimately fit to whatever the data indicates

A lower variance assigns more weight to the prior mean set

Phi dispertion parameter

x row factor = expected losses

y columne factor % unpaid

Models

ODP models

The models give the same reserve estimates as the chain ladder technique (as long as the row and column sums of the incremental claims triangle are positive)

landa age to age factor

ODNB models

Normal distribution

can deal with the problem of negative incremental claims

MSE of the prediction

the expected square difference between the actual outcome and the predicted value

the standard error is the square root of the estimation variance.

The prediction error is concerned with the variability of a forecast, taking account of uncertainty in parameter estimation and also of the inherent variability in the data being forecast