Personal Lines Actuarial Research Department Generalized Linear Models CAGNY Wednesday, November 28,...
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Transcript of Personal Lines Actuarial Research Department Generalized Linear Models CAGNY Wednesday, November 28,...
Personal Lines Actuarial Research Department
Generalized Linear ModelsCAGNY
Wednesday, November 28, 2001
Keith D. Holler Ph.D., FCAS, ASA, ARM, MAAA
Personal Lines Actuarial Research Department
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High Level
e.g. Eye ColorAgeWeight Coffee Size
Given Characteristics:
Predict Response:e.g. Probability someone takes Friday off, given it’s sunny and 70°+e.g. Expected amount spent on lunch
Personal Lines Actuarial Research Department
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Personal auto or H.O. class plansDeductible or ILF severity models Liability non-economic claim settlement amountHurricane damage curves* Direct mail response and conversion*Policyholder retention*WC transition from M.O. to L.T.*Auto physical damage total loss identification*Claim disposal probabilities*
Insurance Examples
* Logistic Regression
Personal Lines Actuarial Research Department
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Example – Personal Auto
Log (Loss Cost) = Intercept + Driver + Car Age Size Factor i Factor j
Driver Age Car Size
Intercept Young Older Small Medium Large
6.50 .75 0 .50 .20 0
e.g. Young Driver, Large CarLoss Cost = exp (6.50 + .75 + 0) = $1,408
Parameters
Personal Lines Actuarial Research Department
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Technical Bits
1. Exponential families – gamma, poisson, normal, binomial2. Fit parameters via maximum likelihood3. Solve MLE by IRLS or Newton-Raphson4. Link Function (e.g. Log Loss Cost)
i. 1-1 functionii. Range Predicted Variable ( - , )iii. LN multiplicative model, id additive model
logit binomial model (yes/no)5. Different means, same scale
Personal Lines Actuarial Research Department
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Personal Auto Class Plan Issues:
1. Territories or other many level variables2. Deductibles and Limits3. Loss Development4. Trend5. Frequency, Severity or Pure Premium6. Exposure7. Model Selection – penalized likelihood an option
Personal Lines Actuarial Research Department
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Why GLMS?
1. Multivariate – adjusts for presence of other variables. No overlap.
2. For non-normal data, GLMS better than OLS.3. Preprogrammed – easy to run, flexible model structures.4. Maximum likelihood allows testing importance of variables.5. Linear structure allows balance between amount of data and
number of variables.
Personal Lines Actuarial Research Department
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Software and References
Software: SAS, GLIM, SPLUS, EMBLEM, GENSTAT, MATLAB, STATA, SPSS
References: Part 9 paper bibliographyGreg Taylor (Recent Astin)Stephen Mildenhall (1999)Hosmer and LemeshowFarrokh Guiahi (June 2000)Karl P. Murphy (Winter 2000)