CAS Exam 8 Fall 2018, Question 1

Study guide: Exam 9

An insurance company is planning to expand into a new territory and has decided to review its historical loss experience in order to determine whether it will require additional capital to support the expansion.

The insurance company has engaged an actuarial consultant to provide insights into a prospective loss ratio for the new territory. The following table outlines the insurance company's historical experience for two long-tailed lines of business (LOB):

Part a (1.5 points)

Conduct chi-square tests with an \alpha value of 0.10 on actual vs. expected claim counts to confirm whether or not risk parameters have shifted over time. Use the following table of critical values:

Part b (1.5 points)

To select an expected future claim frequency for LOB 2, the actuarial consultant has decided to assign equal weight (Z/2) to each of the most recent two groups of accident years and the remaining weight (1-Z) to the overall mean frequency.

Calculate the expected future claim frequency for LOB 2 by first using the mean-squared-error (MSE) criterion to determine the optimal value for Z from the following three choices:

Part c (2.25 points)

(The following information relates to parts c., d., e., f., and g. below)

The insurance company is planning to write $10,000,000 of new business for LOB 1 in the new territory. The following reinsurance treaty options are available to the insurance company to support its expansion:

Option 1: 2,000,000 xs 6,000,000 Aggregate Excess of Loss

• Rate on Line = 12.5%

Option 2: 25% Aggregate Quota Share

• Ceding Commission = 20%
• Target ceded profit of 20%, which specifies that if ceded premiums less ceding commission and ceded loss exceeds 20% of ceded premiums, the excess is paid back to the cedent through a profit commission
• Aggregate Ceded Loss Ratio Cap = 220%

Calculate the ceded profit for each reinsurance option for the following gross loss amount scenarios:

Part d (1.5 points)

The actuarial consultant has decided that a prospective loss ratio of 20% for LOB 1 is appropriate, but that the gross capital required to support the expansion is $8,000,000 based on the insurance company's requirement to hold capital at a 1-in-100 year return period. Assume that aggregate LOB 1 ground-up losses are lognormally distributed.

The cumulative distribution function of a lognormal distribution is: F(x) = \Phi\left(\frac{\ln x - \mu}{\sigma}\right), where \Phi is the standard normal CDF, and \mu and \sigma are the mean and standard deviation of the associated normal distribution.

The mean and variance of a lognormal distribution are given below, as well as a table of values from the standard normal distribution function:

E(X) = \exp\left(\mu + \frac{\sigma^2}{2}\right)

Var(X) = \left[\exp(\sigma^2) - 1\right]\exp(2\mu + \sigma^2)

Determine the coefficient of variation for LOB 1, assuming it is less than 100%.

Part e (1 point)

Calculate the probability of each of the following for LOB 1 assuming aggregate losses are lognormally distributed:

i. Attaching the 2,000,000 xs 6,000,000 Aggregate Excess of Loss treaty

ii. A negative ceded profit on the Aggregate Quota Share

Part f (0.5 points)

State one advantage and one disadvantage of the Aggregate Quote Share (as printed) from the perspective of the reinsurer.

Part g (0.75 points)

Recommend and justify which reinsurance treaty option the insurance company should select for LOB 1. Assume both reinsurance treaty options provide the same amount of capital relief.

Answer this question and see the worked solution

Concepts tested

• Reinsurance Pricing
• Aggregate Excess of Loss
• Quota Share
• Credibility
• Reinsurance Contract Provisions

More questions from this set

• CAS Exam 8 Fall 2018, Question 2