CAS Loss Reserve Seminar Loss Reserving Issues for Small Insurance Companies Patrick J. Crowe, FCAS, MAAA, ARM Vice President and Actuary Kentucky Farm Bureau Insurance

Agenda Ceded Reinsurance Loss Reserve Ranges Materiality

Ceded Reinsurance Develop Direct and Net separately Ceded Estimates Paid Development (Additive, Multiplicative) Incurred Development (Additive, Multiplicative) Bornhuetter/Ferguson Approach Expected Loss Ratio Reinsurer estimates

CASUALTY ACTARIAL SEMINAR LOSS RESERVE RANGES

Approach The model projects lognormal loss development factors for each development period and accident year. The expected mean and standard deviation for the lognormal distribution is selected for each loss development period. Fifty thousand simulations were created for eight situations.

Situations Analyzed 1) Auto #1: Auto Liability Historical incurred loss development patterns for small companies 2) Auto #2: Historical variance to mean ratio increased 100% 3) Auto #3:Historical variance to mean ratio increased 50%

Situations Analyzed 1) Long Tail #1a: Long tail development 2) Long Tail #1b: Long tail development, variance to mean ratio increased 50% 3) Long Tail #1c: Long tail development, variance to mean ratio increased 100%

Situations Analyzed 1) Long Tail #2a: Long tail development increased and variance to mean ratio increased 50% 2) Long Tail #2b: 1) above with variance to mean ratio increased 100%

CAS LOSS RESERVE SEMINAR

LOGNORMAL SIMULATION

CAS LOSS RESERVE SEMINAR

CASUALTY ACTARIAL SEMINAR MATERIALITY

Materiality The viewpoint of some regulators is that he Statement of Opinion is intended to assure the regulator that the Company’s reserve position will be adequate for the next 12 months until a new Opinion is issued. So, those regulators feel the actuary should disclose any reason for concern that the reserves will be materially understated. They want to know if there is a need for close monitoring. Joseph Herbers, 2002 Forum

CAS Loss Reserve Seminar ModelEPSurplusRatioELRCY ULT Auto#128,24521,18475%70%19,771 Auto#228,39021,29375%70%19,873 Auto#328,33921,25475%70%19,837 LT #1a71,73553,80175%70%50,214 LT #1b72,47854,35975%70%50,735 LT #1c73,43955,07975%70%51,407 LT #2a122,11891,58975%70%85,483 LT #2b123,72092,79075%70%86,604

CAS Loss Reserve Seminar ModelCY ULTReservesSDSD/Sur Auto#119,77126,2092, % Auto#319,83726,4533, % Auto#219,87326,3573, % LT #1a50,214102,40713, % LT #1b50,735102,92615, % LT #1c51,407104,38018, % LT #2a85,483184,56729, % LT #2b86,604184,84137, %

CAS Loss Reserve Seminar ModelSD/ Surplus Ceded Recoverable Prem/ Def Res Total/ Surplus Auto#112.6%1.33%5%18.9% Auto#315.5%1.33%5%21.8% Auto#217.7%1.33%5%24.1% LT #1a24.4%1.33%5%30.7% LT #1b28.6%1.33%5%35.0% LT #1c34.3%1.33%5%40.6% LT #2a32.6%1.33%5%38.9% LT #2b40.5%1.33%5%46.8%

CAS Loss Reserve Seminar ModelSubtotal/ Surplus Operating Results Operating % Surplus Total/ Surplus Auto#118.9%5%6.67%25.6% Auto#321.8%5%6.67%28.5% Auto#224.1%5%6.67%30.7% LT #1a30.7%5%6.67%37.4% LT #1b35.0%5%6.67%41.6% LT #1c40.6%5%6.67%47.3% LT #2a38.9%5%6.67%45.6% LT #2b46.8%5%6.67%53.5%

CAS LOSS RESERVE SEMINAR