CAS Exam 8 Fall 2019, Question 7

Study guide: Exam 8

An actuary is pricing a workers compensation policy. Given the following:

Policy Effective Date	January 1, 2020
Policy Term	One year
Annual Loss Trend	4.5%
Cap for individual claims	$100,000
Credibility factor	0.40
Expected ultimate loss before modification	$1,064,000

As of June 30, 2019, ground up reported losses are:

Policy Year	Total Reported Loss	Individual Claims over $100,000
2016	$392,457	$128,305
2017	$1,013,863	$525,626 and $152,860
2018	$459,798	$275,865
2019	$181,325	None

The following limited loss development factors (LDFs) apply to this policy:

Maturity to Ultimate	Limited LDF
42 months	1.052
30 months	1.094
18 months	1.286

Based on an internal study, the actuary believes that claim severity follows a shifted Pareto distribution with $\alpha = 1.3$ and $\beta = 22{,}800$ .

The following expenses apply to this policy:

Loss Adjustment Expense (LAE)	7.5% of loss
Taxes and Fees	3.5% of gross premium
Acquisition	17% of gross premium
Profit and Contingencies	0% of gross premium

Part a (2.25 points)

Calculate the expected ground up reported loss limited to $100,000 per claim for this insured for the three years of experience combined.

Part b (1.5 points)

Calculate the total modified ground up unlimited expected loss for this policy.

Part c (0.25 points)

Alternatively, the actuary could have trended and developed reported losses to the cost level of the prospective policy period. Briefly explain why this approach would not produce an identical modification factor.

Part d (0.5 points)

Calculate the guaranteed cost premium for this insured.

Part e (1.5 points)

The insurer's management is concerned about capacity on risks of this type. To address these concerns, they are requiring facultative reinsurance to support this account. Under the treaty, the reinsurer would assume all aggregate losses between $2,000,000 and $4,000,000. The primary insurer will retain all LAE.

The primary insurer's actuary believes the following Table M and the associated expected loss groupings (ELGs) are appropriate for risks of this type:

ELG	Loss Range
31	$730,000 – 820,000
30	$820,001 – 930,000
29	$930,001 – 1,090,000
28	$1,090,001 – 1,280,000
27	$1,280,001 – 1,515,000
26	$1,515,001 – 1,844,000

Entry Ratio	ELG 31	ELG 30	ELG 29	ELG 28	ELG 27	ELG 26
1.50	0.1876	0.1764	0.1649	0.1529	0.1442	0.1343
1.75	0.1490	0.1376	0.1257	0.1131	0.1048	0.0963
2.00	0.1195	0.1083	0.0964	0.0838	0.0762	0.0692
2.25	0.0968	0.0859	0.0745	0.0623	0.0555	0.0497
2.50	0.0791	0.0687	0.0579	0.0465	0.0404	0.0357
2.75	0.0652	0.0554	0.0453	0.0347	0.0295	0.0257
3.00	0.0541	0.0450	0.0356	0.0260	0.0215	0.0185
3.25	0.0452	0.0367	0.0282	0.0196	0.0157	0.0133
3.50	0.0380	0.0302	0.0224	0.0148	0.0115	0.0096
3.75	0.0321	0.0250	0.0179	0.0111	0.0084	0.0069
4.00	0.0273	0.0207	0.0144	0.0084	0.0062	0.0050

Calculate the loss expected to be ceded to the reinsurer under this treaty. Round to the nearest entry ratio (i.e., do not interpolate).

Part f (1 point)

A reinsurer has quoted a premium of $200,000 for this treaty. Calculate the premium the primary insurer must charge in order to maintain the same underwriting profit.

Part g (0.5 points)

Explain how the assumptions of the primary insurer's actuary may have resulted in an inequitable premium calculated in part f. above.

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