Verall Flashcards
Two important properties of Bayesian model
- Can incorporate expert knowledge
- Can be easily implemented because it’s based on MCMC methods
Common problem with Bayesian method
It can be difficult to derive the posterior distribution, which may be multidimensional
Differences between the chain-ladder and BF method
The BF methods uses an external estimate for the ‘level’ of each row, while CL method uses the data in each row
Describe Mack’s model including advantages and disadvantages
Specifies only the first two moments for the cumulative losses (expected value and variance)
Advantage: the parameter estimates and prediction errors can be obtained using a spreadsheet (it’s simple)
Disadvantage: 1. there is no predictive distribution. 2. additional parameters must be estimated in order to calculate the variance
Describe the ODP model including advantages and disadvantages
It’s model for incremental losses. Using a GLM approach.
The term ‘over-dispersed’ means that the variance is proportional to the mean.
Advantage: 1. reserve estimates are the same as the CL method 2. It’s more stable than the log-normal model
Disadvantage: 1. it requires the column and row sums of incremental values to be positive. 2. It’s hard to see the connection to the CL method from the formulation
Describe the over-dispersed negative binomial model including advantages and disadvantages
Can be applied to both incremental and cumulative losses
Advantage: the mean is exactly the same as the CL method and the reserve estimates are the same as the Cl method.
Disadvantage: the sum of incremental claims down columns must be positive
Describe normal approximation to the negative binomial model including advantages and disadvantages
It replaces the negative binomial with a normal distribution whose mean is unchanged, but the variance is altered to allow for negative incremental claims
Advantage: it allows for negative incremental claims
Disadvantage: additional parameters must be estimated in order to calculate the variance
What is mean squared error of prediction (MSEP)
this is the prediction variance
prediction variance = process variance + estimation variance.
Taking the square root of the MSEP results in the root mean squared error of prediction (RMSEP) or prediction error
Differences between standard error and prediction error
The standard error is the square root of the estimation variance
The prediction error considers both the uncertainty in the parameter estimation and the inherent variability in the data being forecast
The difficulty in calculating the prediction error highlights a few advantages of Bayesian methods
- The full predictive distribution can be found using simulation methods
- The RMSEP (prediction error) can be obtained directly by calculating the standard deviation of the distribution
Two cases of the actuary intervening in the estimation of the development factors for the Cl method
- A development factor is changed in some rows due to external information
- Development factors are based on a five-year volume weighted average rather than all of the available data in the triangle
How does actuary’s strength of the opinion (W) affect the reserve
If W is large (variance of prior distribution of the development factors is large), then development factor will be pulled closer to the chain-ladder LDF and the reserve will closely resemble the CL reserve.
If W is small, the LDF will be pulled closer to the prior mean and the reserve will move away from the CL reserve.
2 options to estimate the column parameters
- Use plug-in estimates from the traditional Cl method with no variability
- Define prior distribution for the column parameters, and estimate the column parameters first, before applying prior distribution for the row parameters and estimating these
The second option is preferred since it allows us to take into account the fact that the column parameters have been estimated when calculating the prediction errors, predictive distributions, etc. This provides a fully stochastic version of the BF method
Examples of when to incorporate expert knowledge or opinion
- Change in payment pattern due to a change in company policy
- Change in benefits due to new laws, requiring adjustments to LDFs
Advantage of a Stochastic Approach
We can produce the full predictive distribution of the reserve, not just the point estimate or the mean and standard deviation
