A5-A10 - Shapland (Monograph #4) Flashcards
What is the Goal of the Over-Dispersed Poisson (ODP) bootstrap model and how does it align with the focus of reserving actuaries in the US?
The Goal is to generate a distribution of possible outcomes, which is meant to provide more information about the potential results.
This doesn’t align with the current focus of reserving actuaries in the US. Their focus is on deterministic point estimates.
List the 2 approaches recommended in the test for applying the ODP bootstrap model to Incurred Losses (as opposed to Paid Losses).
1) Modeling the Incurred data and convert the Ultimate values in a Payment Pattern.
2) Modeling the Paid data and Case Reserves data separately.
Describe the approach of Modeling the Incurred data and convert the Ultimate values in a Payment Pattern for ODP Bootstrapping on Incurred Losses.
- Run the Paid data model in parallel with the Incurred data model
- Use the random payment pattern from each iteration from the Paid data model to convert the ultimate values from each corresponding iteration from the Incurred data to a payment patter for each iteration (for each accident year individually).
What is an “Added Value” of using the approach of Modeling the Incurred data and convert the Ultimate values in a Payment Pattern for ODP Bootstrapping on Incurred Losses.
This process allows the use of case reserves to help predict the ultimate estimates, while still focusing on the stream of payments for measuring risk.
Describe the approach of Modeling the Paid data and Case Reserve Data separately for ODP Bootstrapping on Incurred Losses and its advantage over the alternative approach.
- Apply the ODP Bootstrap to the Munich Chain Ladder Model (see below).
- its advantage is not having to model the paid losses twice, and of explicitly measuring and imposing a framework around the correlation of the paid and outstanding losses.
Munich Chain Ladder Method: estimating ultimate losses using ratios of Paid to Incurred losses.
Can the Bornhuetter-Ferguson or Generalized Cape Cod methods be used with the ODP Bootstrap model?
Yes. The deterministic methods can be worked into the model, and the deterministic assumptions of these methods can be converted into stochastic assumptions.
List an example of how to convert deterministic assumptions into stochastic assumptions for each of the B-F and Cape Cod methods.
B-F: a priori loss ratios can be simulated from a distribution.
Cape Cod: the Cape Cod algorithm can be applied to every ODP bootstrap model iteration to produce a stochastic Cape Cod projection that reflect the unique characteristics of each sample triangle.
List 2 limitations of the Chain-Ladder model (and subsequently the ODP Bootstrap of the Chain-Ladder model).
1) the model doesn’t measure or adjust for Calendar-Year effects
2) it includes a significant number of parameters, and many would argue that it “over-fits” the model to the data.
What is an approach to address 2 limitations of the Chain Ladder model?
Reverting to the original GLM framework.
1) The GLM framework doesn’t require a certain number of parameters so we are free to specify only as many parameters as necessary to get a robust model, which can address the over-fitting issue.
2) The GLM framework affords the ability to add parameters for Calendar Year trends.
What are 2 drawbacks to using a GLM Bootstrap model?
1) the GLM must be solved for each iteration of the bootstrap model, which may slow down the simulation process.
2) the model is no longer directly explainable to others using development factors.
Describe the effect of limiting the number of parameters to accident years in the context of the GLM Bootstrap model has on the common basic assumptions.
In the case of a single accident year parameter, this change moves us away from the common basic assumption of “Each accident year has its own level” and substitutes the assumption that all accident years are homogeneous.
Describe the effect of limiting the number of parameters to developmental periods in the context of the GLM Bootstrap model has on the common basic assumptions.
In the case of a single developmental period parameter, this change moves us away from the common basic assumption of “each development period has a different development parameter”.
What is the byproduct of reducing parameters in the context of residual calculations? Why?
Reduction to 1 parameter for each of the accident years, and developmental periods add 1 more non-zero residual.
This is because, for the change to each dimension, the corners of the triangle (q(1,n) and q(n,1)) are no longer described by a unique parameter (either “alpha” or “beta”).
In the event that we add parameters to account for Calendar Year Trends, what is a drawback, and what is the solution to the drawback?
Adding too many parameters for the number of equations in the model will result in a system that has no unique solution.
To solve for this, some parameters will need to be removed. The text suggests that one starts with a “basic” model with a 1-1-1 (alpha-beta-gamma) parameter framework and add and remove parameters as needed.
