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 Personal Lines Actuarial Research Department 

Generalized Linear Models

CAGNY

Wednesday, November 28, 2001

Keith D. Holler

Ph.D., FCA, AA, A!", "AAA

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 Personal Lines Actuarial Research Department 

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Hi#h $evel

e.#. %ye Color  A#eWei#htCo&&ee i'e

(iven Chara)teristi)s*

Predi)t !es+onse*

e.#. Probability someone taes Friday o&&, #iven it-s

snny and /0

e.#. %+e)ted amont s+ent on ln)h

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 Personal Lines Actuarial Research Department 

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Personal ato or H.4. )lass +lans

Ded)tible or 5$F severity models

$iability non6e)onomi) )laim settlement amont

Hrri)ane dama#e )rves7Dire)t mail res+onse and )onversion7

Poli)yholder retention7

WC transition &rom ".4. to $..7

Ato +hysi)al dama#e total loss identi&i)ation7

Claim dis+osal +robabilities7

5nsran)e %am+les

7 $o#isti) !e#ression

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 Personal Lines Actuarial Research Department 

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%am+le : Personal Ato$o# ;$oss Cost< = 5nter)e+t Driver Car 

  A#e i'e

  Fa)tor i Fa)tor >

Driver A#e Car i'e

5nter)e+t ?on# 4lder mall "edim $ar#e

@.0 ./ 0 .0 .20 0

e.#. ?on# Driver, $ar#e Car 

$oss Cost = e+ ;@.0 ./ 0< = B1,908

Parameters

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 Personal Lines Actuarial Research Department 

 

e)hni)al its

1. %+onential &amilies : #amma, +oisson, normal, binomial

2. Fit +arameters via maimm lielihood

3. olve "$% by 5!$ or Neton6!a+hson9. $in Fn)tion ;e.#. $o# $oss Cost<

i. 161 &n)tion

ii. !an#e Predi)ted Eariable ; 6∞ , ∞ <

iii. $N mlti+li)ative model, id additive model

lo#it binomial model ;yesno<

. Di&&erent means, same s)ale

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 Personal Lines Actuarial Research Department 

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Personal Ato Class Plan 5sses*

1. erritories or other many level variables

2. Ded)tibles and $imits

3. $oss Develo+ment

9. rend

. FreGen)y, everity or Pre Premim

@. %+osre

/. "odel ele)tion : +enali'ed lielihood an o+tion

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 Personal Lines Actuarial Research Department 

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Why ($"

1. "ltivariate : ad>sts &or +resen)e o& other variables. No

overla+.

2. For non6normal data, ($" better than 4$.3. Pre+ro#rammed : easy to rn, &leible model str)tres.

9. "aimm lielihood allos testin# im+ortan)e o& variables.

. $inear str)tre allos balan)e beteen amont o& data and

nmber o& variables.

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 Personal Lines Actuarial Research Department 

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o&tare and !e&eren)es

o&tare* A, ($5", P$I, %"$%",

(%NA, "A$A, AA, P

!e&eren)es* Part J +a+er biblio#ra+hy(re# aylor ;!e)ent Astin<

te+hen "ildenhall ;1JJJ<

Hosmer and $emesho

Farroh (iahi ;ne 2000<Karl P. "r+hy ;Winter 2000