Verrall Flashcards
Examples where using expert knowledge to adjust the model may be desirable
- There has been a change in payment pattern
- New legislation limits benefits
–> decreases the potential for loss development and development factors must be adjusted
Benefit of a Bayesian model over Mack or Bootstrap to predict values
Can incorporate expert opinion into the model naturally without compromising the underlying assumptions
two key areas:
- Expected losses in the BF method
- Selected individual LDFs in the chaim ladder
Mack stochastic model for the Chain Ladder model
Mack stochastic model: advantages and disadvantages
Advantages:
easy to implement
Parameter estimates and prediction errors (reserve ranges) can be calculated in a spreadsheet
Disadvantages:
Since a distribution isn’t specified, no specify distribution
Separate parameters for the variance must be also estimated apart from the LDFs
Over-Dispersed Poisson model for incremental loss: GLM approach
Incremental losses (Cij) are modeled with an independent ODP model with mean mij and dispersion factor
Over-Dispersed Poisson model for Chain Ladder method: Row-Column approach
Cij ~ Independent Over-Dispersed Poisson
xi - Expected ult loss for accident year i up to the last development period of the triangle
yi - % of ultimate loss emerging in development period j
Over-Dispersed Poisson model: Advantages and Disadvantages
Advantages:
Doesn’t necessarily break down if there are some negative incremental values
Gives the same reserve estimate as the chain ladder
More stable than lognormal model of Kremer
Disadvantages:
Connection to the chain ladder method is not immediately apparent
Over-Dispersed Negative Binomial distribution model of incremental losses
- reserve estimates are the same as Chain Ladder
- all LDfs must be >1 (no overall negative development) or variance’d be negative
Over-Dispersed Negative Binomial model of incremental losses: advantages and disadvantage
Advantage:
Doesn’t necessarily break down if there are some negative incremental losses
Gives the same reserve estimate and has the same form as the Chain ladder method
Disadvantage
Column sums of incremental losses must be positive (or variance would be negative)
Model of losses using Normal distribution
Allows negative incremental losses
Cij ~ Normal with below
Prediction error of a reserve
Prediction Error = Root mean square error of prediction
Difference between prediction error and standard error
standard error = sqrt (estimation variance)
Standard Error only accounts for the parameter estimation error
Prediction error is concerned with the variability of the forecast and accounts for both:
Uncertainty in the parameter estimation (Estimation variance)
Variability in the data being forecast (process variance)
Advantage of Bayesian methods for calculating prediction error
Can use simulation to find the full predictive distribution of reserves
this is preferable than just knowing the mean/variance of distribution
Can calculate RMSEP (prediction error) directly by calculating the standard deviation
Two common ways to incorporate expert opinion about LDFs
Actuary overrides a development factor in a particular row (accident year)
-> if there is information that different LDFs should be used in some rows
Actuary uses a 5-yr volume-wtd (or n-yr) average for the selected LDFs as opposed to the all-yr avg
Bayesian model for the BF method formulas
Credibility-weighted bayesian model for the BF method formulas
Fully stochastic BF model formulas
