Clark Flashcards
Advantage of using parameterized curves to describe the emergence pattern
- Estimation of unpaid is simple since we only have to estimate two parameters
- We can use data that is not from a triangle with evenly spaced evaluation date
- The payout pattern G(x) is smooth, and does not overfit like age-to-age factors might
Two key elements of a statistical loss reserving model
- The expected amount of loss to emerge in some time period
- The distribution of actual emergence around the expected value
Describe the LDF method to estimate the loss emergence amount
Assumes the loss amount in each AY is independent from all other years (this is the standard chain-ladder method)
Describe the Cape Cod Method to estimate the loss emergence amount
Assumes that there is a known relationship between the expected ultimate losses across accident years, where the relationship is identified by an exposure base (OLP)
Advantage of Cape Cod method over LDF method
- The Cape Cod method is preferred since data is summarized into a loss triangle with relatively few data points. Since the LDF method requires an estimation of a number of parameters, it tends to be over-parameterized when few data points exist.
- The Cape Cod method has a smaller parameter variance. The process variance can be higher or lower than LDF. In general, the Cape Cod method produces a lower total variance than the LDF method
What is driving the lower parameter variance for Cape Cod method
- reduced number of parameter
- incorporation of additional information from the exposure base
2 Key advantages of using the over-dispersed Poisson distribution to model incremental losses
- Inclusion of scaling factors allows us to match the first and second moments of any distribution, allowing high flexibility
- Maximum likelihood estimation produces the LDF and Cape Cod estimates of ultimate losses, so the results can be presented in a familiar format
Advantage of maximum loglikelihood function
It works in the presence of negative or zero incremental losses since we never actually take the log of the actual incremental loss
Key assumptions of loss emergence model
- Incremental losses are independent and identically distributed (iid)
- The variance/mean scale parameter is fixed and known
- Variance estimates are based on an approximation to the Rao-Cramer Lower bound
-The model assumptions mean there is a potential that future losses have higher variance than what the model indicates
Plot the residuals against a number of things to test model assumptions
- Increment age (checks for development period over/under estimated)
- The expected loss in each increment (to test if variance/mean ratio is constant)
- Calendar Year (checks for diagonal effects)
Overall, we want the residuals to be randomly scattered around the zero line
Major reason for calculating the 12-month development (calendar year development)
the estimate is testable within a short timeframe.
When does MLE model works the best
When using a tabular format of data rather than a triangular format.
So we can use data at irregular evaluation periods or when you don’t have the full triangle
Why the paper focuses on the loglogistic and weibull browth curves
For both curves
1. Smoothly move from 0% to 100%
2. Closely match the empirical data
3. First and second derivatives are calculable
Which one is larger, parameter variance or process variance
The parameter variance is generally larger than the process variance (few data points, so more uncertainty coming from parameter estimation than random events)
Comparing the CV between discounted reserves and undiscounted reserves
The CV for discounted reserves is lower since the tail of the payout curve has the greatest parameter variance and also received the deepest discount
