Assume XYZ Insurance Company began writing Commercial Umbrella business=
in
1988 and expects an ELR of 0.700.
Industry Umbrella Loss Development Factors used to proxy this company?s=
expected development=3D
@12 mo. 10.000 @72mo. 1.333
@24 mo. 5.000 @84mo. 1.250
@36mo. 2.500 @96mo. 1.176
@48mo. 2.000 @108mo. 1.111
@60mo. 1.429 @120mo. 1.053
As of 12/31/97 AY Paid + Case Reserve Loss Ratio =3D 0.00 for all years=
, 1988
? 1997.
Calculate the expected 1992 Ultimate Loss Ratio @12/31/97.
page down for assumed answer.
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Since (1) data is extremely thin, calculating IBNR based on indicated c=
ase
incurred is not appropriate, and (2) this is an unusual line with a lon=
g
tail, need to use the Bornhuetter/Ferguson Method.
AY 1992 @ 12/31/97 is valuated at 72 months.
Indicated IBNR =3D Earned Premium x ELR x (1 ? 1/LDF)
Expected Ultimate Losses =3D Incurred Losses + Indicated IBNR
Expected Ultimate Losses =3D 0 + Earned Premium x ELR x (1 ? 1/LDF=
)
Expected Ultimate Loss Ratio =3D Expected Ultimate Losses / Earned=
Premium
Expected Ultimate Loss Ratio =3D ELR x (1 ? 1/LDF)
Expected Ultimate Loss Ratio for AY 1992 valued at 12/31/97 =3D
0.70 x (1 ? 1/1.333) =3D 0.175; Pages 186-187
=