Taylor, Verrall, Marshall

Question 1

Exponential Dispersion Family

Answer 1

Theta: Location Parameter
Phi: Scale/Dispersion Parameter
b: Shape function
c: Normalizing function (unit total mass)
V: Variance function

Question 2

Tweedie Sub-Family

Answer 2

Restricts V = mu^p

Where
p=0 Normal
p=1 ODP
p=2 Gamma
p=3 Inverse Gaussian

Question 3

GLM Specifications

Answer 3

Error dist.
Explanatory variables
Link function

Question 4

Standardized Pearson vs Standardized Deviance Residuals

Answer 4

SPR: Reproduces any dist. in original data

SDR: Normal, more useful for model assessment

Question 5

GLM Value Correction

Answer 5

Outliers: 0 weight

Large variance: Less weight

Question 6

Parametric Mack Model

Answer 6

Remove variance assumption
Define Next Incr.| Cuml. as an EDF dist.

Question 7

Theorem: Parametric Mack Model

Answer 7

1. If original variance assumption holds: MLEs of parametric Mack are CL LDFs
2. If dist. is restricted to ODP AND dispersion params only vary by column:
   -CL LDFs are MVUEs
   -Cuml. loss and reserve estimates are MVUEs

This is stronger than non-parametric Mack model (unbiased but min variance of only linear combos of LDFs)

Question 8

Cross-Classified Model Assumptions

Answer 8

1. Incr. loss stochastically independent
2. Incr. loss dist. in EDF
3. Expected Incr. = Alpha_AY * Beta_Dev
4. Sum of beta’s = 1

Question 9

Theorems: Cross-Classified Model

Answer 9

1. If ODP AND dispersion parameters all equal:
   -MLEs same as CL LDFs
2. If ODP AND dispersion all equal AND fitted values corrected for bias:
   -they are also MVUEs

Implies:
-Forecasts from parametric Mack and ODP Cross-Classified and Chain Ladder all the same
-Can forecast from ODP Cross-Classified while working as if ODP Mack

Question 10

When to incorporate expert opinion

Answer 10

1. Change in payment pattern
2. Change in benefits due to legislation

Question 11

Ways to incorporate expert opinion

Answer 11

1. Override LDFs in particular row
2. Use only n-year averages for LDFs
3. Choose a different a priori estimate for BF

Question 12

Types of Stochastic Models

Answer 12

1. Mack
2. ODP
3. Over-Dispersed Negative Binomial
4. Normal Approx. to Negative Binomial

Question 13

Stochastic Mack Pros and Cons

Answer 13

Pro
-Easy

Cons
-No predictive dist. specified
-Need to estimate parameters for variance separate from LDFs

Question 14

Stochastic ODP Pros and Cons

Answer 14

Pros
-Can handle some negative incr.
-Same reserve estimate as CL
-More stable than lognormal

Con
-Difficult to explain (Less connected to CL)

Question 15

Stochastic OD-Neg-Bin Pros and Cons

Answer 15

Pros
-Can handle some negative incr.
-Same reserve estimate as CL
-Same form as CL

Con
-Can’t handle negative column sums (negative variance)

Question 16

Stochastic Normal Approx. Pros and Cons

Answer 16

Pro
-Can handle all negative incr. values

Con
-Need to estimate a separate parameter apart from LDFs

Question 17

Prediction Error vs Standard Error

Answer 17

PE: Both process and parameter variance
SE: Parameter only

Question 18

Bayesian Model for BF

Answer 18

Pros
-Adjust credibility by changing beta (Increase=Smaller Prior=Lower Cred=Closer to BF)

-Fully predictive dist. of reserve

Question 19

Independent Risk Components

Answer 19

Parameter Risk
Process Risk

Question 20

Internal Systemic Risk Components

Answer 20

Specification Error: From inability to perfectly model insurance process

Parameter Selection Error: From inability to adequately measure all predictors of cost outcomes

Data Error: From lack of data or knowledge needed for analysis

Question 21

External Systemic Risk Components

Answer 21

-Economic
-Event
-Legislative
-Latent claim
-Recovery
-Expense
-Claim management process change

Question 22

Measures of Specification Error

Answer 22

-Number independent models
-Range of results from models
-Reasonability checks of model results

Question 23

Measures of Parameter Selection Error

Answer 23

-Best predictors identified
-Best predictors stable over time

Question 24

Measures of Data Error

Answer 24

-Good knowledge of past processes
-Timeliness, consistency, reliability of data
-Appropriate reconciliation of data