Verrall Flashcards
BF Model Setup
Solution using only row parameters
Expected incremental losses using y parameters
If we want the reserve estimate to be base on the loss data, what assumptions should we make?
Calculate y3
Describe the MCMC methodology.
MCMC methods simulate the posterior distribution of a random variable by breaking the process down in a number of simulations. This is achieved by using the conditional distribution of each parameter (given all of the others), making the simulation a univariate distribution. Considering each parameter in turn creates a Markov chain
Identify four stochastic models for the chain-ladder technique. For each model, provide one disadvantage.
⇧ Mack’s model – no predictive distribution
⇧ Over-dispersed Poisson distribution – requires the sum of the incremental values down a column to be positive
⇧ Over-dispersed negative binomial distribution – requires the sum of the incremental values down a column to be positive
⇧ Normal approximation to the negative binomial model – additional parameters must be estimated in order to calculate the variance
Provide the formula for the prediction variance.
Prediction variance = process variance + estimation variance
Explain the difference between the standard error and the prediction error. (Verrall)
The standard error considers the uncertainty in parameter estimation, whereas the prediction error considers both the uncertainty in parameter estimation and the inherent variability in the data being forecast
Provide two advantages of Bayesian methods.
⇧ The full predictive distribution can be found using simulation methods
⇧ The prediction error can be obtained directly by calculating the standard deviation of the predictive distribution
Fully describe the steps required to implement a Bayesian model for the Bornhuetter/Ferguson method. Assume that prior distributions are defined for the column parameters and the row parameters.
⇧ Define improper prior distributions for the column parameters and estimate the column parameters first. Since we are using improper prior distributions with large variances, the estimates will be those implied by the chain-ladder method
⇧ Define prior distributions for the row parameters xi. In practice, these are often defined as gamma distributions where the B parameter controls the level of confidence in the prior information
⇧ Using the xi, re-parameterize the model in terms of “Y”i. We must do this since we defined prior distributions for the column parameters
Mack’s Model (Verrall)
ODP (Verrall)
OD - Negative Binomial (Verrall)
Normal Approx. to the Negative Binomial (Verrall)
