univariate and multivariate

Question 1

3 main approaches for univariate

Answer 1

1. Pure premium: calc PP for each level of RV and then divide by base level or overall PP to get indicated relativities
2. Loss ratio: calc LR for each level of RV then divide by base level or overall LR to get indicated relativities
3. Adjusted pure premium: adjust exposures by weighted average current relativity from other RVs and then use PPA using adjusted exposures

Question 2

main distortion in PPA

Answer 2

-main distortion in PPA=assumes no correlation between exposures for different RVs (distributional bias)

Question 3

distributional bias

Answer 3

if exposures of RV are correlated with exposures of the levels of another RV, then approach will double count experience of those levels

Question 4

why is LRA improvement over PPA

Answer 4

because it attempts to correct for distributional bias -> uses premium instead of exposures and prem reflect higher levels of prem obtained within class as result of correlation with other higher rated levels of other RVs

Question 5

problem with APPA

Answer 5

calc weighted average relativities can be cumbersome in a rating plan with many variables

Question 6

adjustments before applying univariate approaches

Answer 6

• large events and anomalies: large losses and CAT should be removed and possibly replaced with some sort of longer-term loading
• one-time changes: class data should be adjusted for all past one-time changes
• continuous changes: trending of prem and loss is often ignored since common assumption=all classes are trending at same rate
• development: often ignored since common assumption=all classes are developing at the same rate
• expenses and profit: assumed to not vary by class so analysis often done using reported loss and sometimes ALAE; if FEs are material and separate expense fee is not using in rating algorithm, then relativities should be adjusted for FEs
• credibility: individual classes have less data, they are less credible, so credibility weighting becomes more important

Question 7

credibility with PPA

Answer 7

credibility is applied to indicated relativity to total (compliment is normalized relativity = current relativity/total current relativity)

Question 8

credibility with LRA

Answer 8

credibility is applied to rel change factor (compliment is no change aka change factor of 1)

Question 9

problem with univariate approaches

Answer 9

• univariate does not properly account for impact of correlated variables
• many variables in insurance are correlated

Question 10

multivariate analysis incorporates

Answer 10

impact of multiple variables simultaneously

Question 11

why have GLMs grown in popularity

Answer 11

as result of increased computing power, better data availability, and competitive pressure to avoid adverse selection

Question 12

benefits of GLMs

Answer 12

Properly adjust for exposure correlations btw RVs

Attempt to focus on signal and ignore noise in data

Provide statistical diagnostics like CIs

Allows for consideration of interactions btw RVs

Question 13

exposure correlation

Answer 13

relationship btw 2 exposures of 2 or more RVs

Question 14

response correlation

Answer 14

when effect of 1 variable varies based on levels of another variable

Question 15

minimium bias procedure

Answer 15

• iterative univariate methods that properly adjust for exposure correlation
• set total reported loss&ALAE for group = total prem you would obtain form that group with indicated relativities, ex:

total loss for t1=curr base rate*t1*sum(exposuresi *ci)

-start with seed values (based on univariate analysis) of class relativities and solve for territory relativities and repeat until convergence

Question 16

problem with minimum bias procedure

Answer 16

do not provide ways to test for whether variables are stat significant and they are computationally inefficient

Question 17

sequential analysis

Answer 17

• sequence of using APPA on different variables
• only class RMing allowed for CA personal auto
• start with standard univariate analysis to obtain relativities for single variable and then perform APPA for second variable and so on

Question 18

sequential analysis problems

Answer 18

• does not deal with exposure correlation
• no closed form solution so results changes based on order of variables chosen

Question 19

GLMs seek to express

Answer 19

express formulaic relationship between multiple predictor variables and response variable such as PP, freq, or severity

• link fct is often log link function which assumes RVs are multiplicative
• GLMs not run on LRs because no need to OLP @ granular level

Question 20

important steps of GLM

Answer 20

-important steps: compile dataset with enough data for modeling, selecting link fct, specifying distribution of underlying random process, using maximum likelihood to calc parameters of model

Question 21

if noticeable difference between one-way and GLM results

Answer 21

suggests RV is correlated with other RVs and one-way analysis is not fully accounting for correlation

Question 22

if GLM gives counterintuitive results like higher deductible has higher relativity/costs more

Answer 22

could be symptom of limited data @ that level

do not implement result

Question 23

if 2 levels’ CIs have 1 in it

Answer 23

suggests there is no significant difference between the impact of those levels

Question 24

common diagnostics for GLMS

Answer 24

• running model on separate consecutive time periods of data to see if estimated parameters are consistent over time
• building model on 1 subset and then comparing predictions with actual results on second subset of data (holdout sample) -> can see if over or under fitting

Question 25

Data mining techniques

Answer 25

• factor analysis: reduce number of variables needed in classification RM analysis
• cluster analysis: combine similar risks into groups
• CART: build if-then rules for use in classification
• MARS: helps turn continuous variables into categorical
• neural networks: training algorithms are given set of data and identify patterns -> help identify previously unknown interactions between variables