ACTUARIES & DATA SCIENCE Jerome Tuttle, FCAS, CPCU - - PowerPoint PPT Presentation

ACTUARIES & DATA SCIENCE

Jerome Tuttle, FCAS, CPCU Retired Actuary

1

What i is an an act actuar ary?

• The

m mathematicia icians ns

• f

the i insurance ce i industry.

• A

business p professiona nal wh who deals wit with t the f fina inanc ncial im impact

• f

ris isk a and nd unce ncertaint nty.

• Anal

alyz yzes, m man anag ages, an and meas asures t the f finan ancial i impac pact

• f

ri risk an and u uncertai ainty. y.

• Develo

elops a and validates es m models ls a and commu municates es r result lts t to guide d decis isio ion-making king.

• Act

ctuaries in in movie ies:

2

Jack N k Nicholson n – Ben S Stille ller – About Sc Schmidt (200 2002) A Alo long Ca Came Polly lly (200 2004)

Insu nsuranc nce is is a uniq nique b busine siness ss

• We

d don’t n’t kno know

• ur

co cost (cl (claims) wh when we we sell t the p policy icy, a and nd wit with s some cl claim ims we we don’t n’t kno know for many ny years.

• We

We a are not required to to se sell to to everyone – similar ar t to ban ank l loan ans and college a admissi ssions. s.

• We

do do not char arge t the s sam ame pri price t to everyo ryone. This i is RE REQUIRE RED b by law aw, e e.g., F FL Statute 6 627.062:

■

Ra Rates m may ay not be u unfai airl rly di discri riminatory. ry.

■

A rate is is unf nfair irly d dis iscr criminatory t to a group

• f

ris isks ks i if the rate te d does n not be bear a a reasonable r relationship to to the the expe xpected l loss e expe xperience am among t the ri risks.

3

$$$$$ $$$

The he i interse secti tion a among math/ th/sta stats, ts, c compute ter s sci, & subject ct m matter k knowledge t to extract ct m meaning ningful i insig ights from data ta tr transl slating i into to ta tangible bu business v value.

What is da data ta s science?

4

Exam amples

• f
• f

data sci cience ce e

• Interne

net s search ch e engine ine a algorit ithms.

• Tar

argeted adv advert rtising an and recommenda dations.

• Tar

arget S Stores s sent di diape aper c coupo pons t to the pr pregnan ant t teenager be before she she to told he her f fath ther. (Fo Folklore?)

• Moneyb

yball an and spo port rts an anal alyt ytics.

• Bette

tter s singles m matchi hing

• n

dating w websi bsite tes. s.

• Diseas

ase di diag agnosis, pe pers rsonal alized h heal althcar are r recs.

• Data

dri driven c cri rime pr predi diction, f fac acial al r recognition, t terr rrori rist forecasts. sts.

• Which

t twe weets d did id Trump wr writ ite, a and nd wh whic ich d did id his is s staff wr writ ite?

5

Act Actuar aries an and data sci cience ce

• “Act

ctuaries we were a among ng t the f fir irst d data sci cient ntists.” (C (Colin P Prie iest, ac actuary ary turn rned da data scientist a at Data Ro Robot, S Singapo pore.)

• Actuari

aries ar are strongest a at math/stat an and do domai ain k knowledg dge (we s study i insurance, b besi sides m math/ h/sta stat). t).

• Data

s scient ntis ists a are strong ngest a at computer s science nce, e especia cially co coding ing, d data m manip nipulation a and nd joinin ining t tables, t theory

• f

machine ine l learning ning ( (training ing v versus t testing ing,

• vertraining

ining), a and machine ine l learning ning a algorit ithms.

• Actuari

arial exam xams n now i include de: Gener erali lized ed linea ear m models ls, K K-nearest st n neighbo bors, s, K K-mea means clusteri ring, B Baye ayes c clas assifier, r, de decision t trees, r ran ando dom f forest, pri principa pal c compo ponent an anal alys ysis. Also a a pr predi dictive an anal al spe pecialty. y.

6

Rando domly s spl plit da data ta into to tr training versus us te testi ting da data ta

7

RMSE

• n

n test d data = = √[∑ (A (Act ctual – Predict icted)2 / n] n]

8

Som

• me

act actuar arial e exam amples

• f
• f

data s sci cience ce t tech chniques

• If

predict ctiv ive m modeling ing r refers t to estim imating ing i insurance nce c costs, t then ac actuari aries h hav ave b been do doing t this f forever.

• Today

p predict ctiv ive m modeling ng i is computatio iona nally i intens nsiv ive,

• ften

testi sting a all possibl ble p permuta tati tions

• f

variabl bles, s, t transformati tions, s, etc

• The

2 2 broad ad c categori ries i in da data science ar are pr predi diction an and classifica ication. Classif ifica icatio ion i is p predict cting ng a a category.

• Pr

Prediction

• n
• ft
• ften

i invol volve ves t types

• f
• f

regression. . Linear r regression i is bei eing r rep eplaced b by mo more f flex lexible Ge Generalized L Linear M Models els.

• Classif

ifica icatio ion i includes: Decis cisio ion t trees: underwr writ iting ing Clustering ing: territ itorie ies Pri rincipa pal c compo ponent an anal alys ysis: de detect f frau aud

• In

the f following e exam xamples, as assume n n inde dependent v vari ariab ables an and p da data v val alues.

9

For

• r

i insuran ance ce rating, we grou

• up

(h (hop

• pefully)

similar cu custom

• mers

into cl clas asses an and ch char arge an an av averag age rate for

• r

the cl clas ass. Clas assifica cation is rar arely p perfect ct.

Before classif ifica icatio ion After classif ifica icatio ion

Insu nsuranc nce cla lasses sses may inc inclu lude age, e, gend ender, urban / / rur ural te territory, y, marita tal sta tatus tus, miles dr driven, claims histor

• ry,

car car type, car car ag age, e etc. c.

But w within in e each ch n n-dim imensiona nal s slic ice, t there is is s stil ill co cons nsiderable vari ariab ability. y. A compan pany w wan ants t to choose t the b better t than an av averag age c customers within e eac ach c clas ass t to mak ake a a pr profit.

10

Gener eneralized L Linea inear M Models: els: pric icin ing

• Tradit

itionally we we u used cl classical l line inear r regression, n, a and nd we we t treated

• ur

pricing ng b by class a as multip iplica icativ ive:

• Ba

Base se rate te = = $ $100 Times fa factor

• r

f for

• r

Age i i = 1.5 .50 Times fa factor

• r

f for

• r

Gender j j = 1.2 .20 Times fa factor

• r

f for

• r

Territor

• ry

k k = 1.4 .40, ... ... , etc.

• This

di disregar ards ds i interac actions b between c clas asses an and mak akes as assumptions

• n

norm rmal ality an and common v vari arian ances.

• GLMs

co cons nsis ist

• f

wid wider r rang nge

• f

models wit with r response v varia iable as assumed t to be a a member

• f

expo xponential f fam amily. y.

• Re

Results i in some f fac actors rs b being r redu duced,

• thers

i increas ased. d.

• Other

appl applications

• f

GLM LM: Effect ct

• f

telematics ics

• n

claim ims Unde derw rwri riting s score c car ards ds Predict ict c claims l like kely t to settle f far above t their ir i initia ial e estim imate

11

12

Dec ecisio ision t trees: ees: und nder erwritin ing

• Sequ

quen entially lly s splits d data into c categ egories es h having s simi mila lar v values es f for de depe pendent v vari ariab ables.

• Use

Uses sta statistic su such a as Gini In Index to to do sp split.

• Possible

v vari ariab ables:

• no. ye

years ars r renewed,

• ccupa

pation, pr premium paym payment h history, ry, t telematics ( (spe peed, b brak aking, t time

• f

day, day, etc.)

13

Clus uste tering: te territories

• Parti

titions d data ta into to c classes ba base sed

• n

ho how c close sely d data ta i is grouped ed. Iter eratively ely u updates es c center ers a and re-parti titi tions. s.

• There

i is n no de depe pende dent v vari ariab able.

• Ano

nother u use is is cl clustering s sim imilar

• ccu

ccupations ns.

• Flori

rida da h has as 2 28 r rating terr rritori ries i in au auto.

Yao, J. (2008). Clustering in ratemaking; applications in territories clustering. Casualty Actuarial Society Predictive Modeling Seminar

14

Princi cipal com compon

• nent

an anal alysis: frau aud detect ction

• n
• Re

Redu duces a a lar arge n

• no. of

vari ariab ables t to a smal aller n no.

• f

mutually lly u uncorrela lated ed v variable les t that p preser erves es as as m much v vari ariab ability as as po possible.

• Auto

f fraud (s (staged a accid ccident, inf inflated b bil ills, co collusive medical

• r

bo body sho shops) ha hard to to dete tect by by first st-level c l claim m exam xaminers rs.

• No

de depe pendent v vari ariab

• able. D

Data do doesn’t s say ay which c clai aim i is defi finitely fr fraud ud. . Muc uch fr fraud ud is un undetected.

• Data
• ft
• ften
• r
• rdinal,

e e.g .g. s . sus uspicion l level = = {1, 2 2, …, …, 5} f for

• r

eac ach vari ariab able ( (# chiroprac actor v visits, h hi v vol med pr provide der) r).

• Goa
• al

i is

• ve
• verall

fr fraud ud sus uspicion

• n

s scor

• re,

iteratively w weighting ind indiv iv v varia iables b based

• n

their co cons nsistenc ncy a and nd co correlation to

• ve
• verall

s scor

• re.
• Why

Why d do we stu study L Linear Al Algebra? PCA u use ses

• rtho

thogonal transformati tions, s, e eigenvecto tors. s.

15

Credi dit s scoring

• A

numerica ical s score

• f

a person’s n’s c credit itwo worthine iness. Ideally corr rrelates w with c clai aims e expe xperi rience an and pr provide des addi additional al pr predi dictive ab ability b beyo yond t tradi aditional al r rating v vari ariab ables.

• Perm

rmitted b by FL Statute 6 626.9741.

• Crit

iticized a as unf nfair ir t to mino inorities a and nd low-income me p people, le, al although an anal alys ysts di dispu pute t the c cri riticism.

• Variabl

bles include d debt/ bt/asse sset r ratio, l late te payment h histo story…

• Data

s science nce t tech chniq niques: clusters, t trees, G GLM, M, P PCA, … … ■ Lo Loss r ratio = f (vari ariab ables X X1, … …, Xn)

• Oft

ften us used i in the d decision

• n

w whether

• r
• r

not

• t

to

• ffe
• ffer

insu surance, bu but n not use sed to to dete termine the the p price.

• Man

any pu publicly av avai ailable c credi dit ri risk da datab abases f for credi dit car ards ds an and loan ans, e e.g., Kag aggle c compe petition a at Kaggle. ggle.com/c m/c/G /GiveM eMeSo eSomeC meCred edit/ ■ Pr Prob

• bability
• f
• f

defa faul ult = = f (va variables X X1, …, …, Xn)

16

Text An Anal alysis

• Mo

Most data is is nu numerical and nd is is ne neatly ca captured in in f fie ields

• Fre

ree-for

• rm

text i is a pot

• tential

g gol

• ld

m mine

• f
• f

infor

• rmation
• n,

b but ut i it requ equires ef effort t to ex extract go gold ld n nugg ggets.

• Misspelli

ellings gs, s synonyms, s stems ems l like “ “ing ing” an and “e “ed” d”, e etc.

• Look
• ok

for

• r

fr

• freq. w

. wor

• rds,

g group

• ups
• f
• f

wor

• rds

appearing t tog

• gether.
• What

k kinds ds

• f

clai aims ar are

• ccurri

rring? “W “Water” r” m may ay be a a captured ed f field ld, b but “water er & & baseme ement”

• r

“water er & & ceili ling” g” may be m more h helpful in in find indin ing t trends.

• What

w words ds s signal po potential al l lar arge c clai aim am amount?

• How

do do pe peopl ple f feel ab about i insuran ance ads ads? Ide dentify senti timents ts i in custo tomer s surveys & & tweets. ts.

• FL

Statute 627.4145 r requir ires i insurance nce p policie cies h have m min 4 45 score

• n

Flesc sch r readabi bility t test. st.

17

Ref Refer eren ences

• Frees,

E.

• E. W.,

.,

• et. a

. al. . (2016). Pr . Predictive m mod

• deling

appl applications i in ac actuari rial al s

• science. N

New Y York rk: Cambr bridge U Universi sity ty Press. ss.

• Healy,

K K. . (2018). D Data vi visua ualization

• n. Pr

. Princeton

• n,

NJ.: P Princeto ton U Universi sity ty P Press. ss.

• James,

G G., ., e

• et. a

. al. . (2017). A An introd

• duc

uction

• n

t to statis istical l learning ing w with a applic icatio ions ns i in

• R. New

York rk: S Spri pringer

• Zh

Zhao ao,

• Y. (

(2013). R an and da data m

• mining. San

an D Diego: Academic P Press. ss.