loss aggregate part3

7/25/2019 Loss Aggregate Part3

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Modeling Property Treaties withSignifcant Cat Exposure

Model non-cat & cat LRs separately

!on Cat LRs ft to a lognor"al cur#e

Cat LR distri$ution produced $y co""ercialcatastrophe "odel

Co"$ine %con#olute the non-cat & cat loss ratiodistri$utions


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Con#oluting !on-cat & Cat LRs- Exa"ple

0% 30% 60% 100%

LR Prob 60% 20% 15% 5%

40% 10% 6.0% 2.0% 1.5% 0.5%

55% 25% 15.0% 5.0% 3.8% 1.3%65% 35% 21.0% 7.0% 5.3% 1.8%

77% 25% 15.0% 5.0% 3.8% 1.3%

100% 5% 3.0% 1.0% 0.8% 0.3%

These probabilities 40% 70% 100% 140%

correspond to 55% 85% 115% 155%

these total LR's 65% 5% 125% 165%

77% 107% 137% 177%

100% 130% 160% 200%

Total Loss Ratios

!isreti"ed #at LR's

$on cat


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Truncated Loss Ratio'istri$utions

Pro$le"( To reasona$ly "odel the possi$ility o)high LR re*uires a high lognor"al C+

,igh lognor"al C+ o)ten leads to unrealisticallyhigh pro$a$ilities o) low LRs which o#erstatescost o) PC

Solution( 'ont allow LR to go $elow selected"ini"u" e.g.. /0 pro$a$ility o) LR12/0

3d4ust the "ean loss ratio used to calculatethe lognor"al para"eters to cause the

aggregate distri$ution to pro$a$ility weight$ac5 to initial expected LR


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Su""ary o) Loss Ratio'istri$ution Method

3d#antage(

Easier and *uic5er than separately "odeling)re*uency and se#erity

Reasona$le )or "ost pro-rata treaties

6sually inappropriate )or excess o) loss contracts 'oes not re7ect the hit or "iss nature o) "any

excess o) loss contracts

6nderstates pro$a$ility o) 8ero loss

May understate the potential o) losses "uch

greater than the expected loss


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Excess o) Loss Contracts( SeparateModeling o) 9re*uency and Se#erity

6sed "ainly )or "odeling excess o) loss contracts Most aggregate distri$ution approaches assu"e

that )re*uency and se#erity are independent 'i:erent 3pproaches

Si"ulation %9ocus o) this presentation !u"erical Methods ,ec5"an Meyers ; 9ast calculating approxi"ation to

aggregate distri$ution Pan4er Method ;

Select discrete nu"$er o) possi$le se#erities %i.e. create

loss aggregate part3

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