CAS Exam 8 Fall 2015, Question 21

Study guide: Exam 9

A reinsurer is offering a ceding company a two-year aggregate stop loss with the following terms:

The treaty is effective on 1/1/2016 and expires on 12/31/2017.
The treaty will cover aggregate losses between a 65% and a 70% loss ratio for accident years 2016 and 2017 separately.
Premium is paid at the beginning of each year and all losses are paid at the end of the year incurred.

Additionally, the reinsurance treaty has the following termination provisions:

The ceding company has the option to terminate the contract at the end of 2016 and receive a profit commission from the reinsurer calculated as follows:
- Profit commission = [35% * 2016 Ceded Premium] – [2016 Ceded Loss], subject to a minimum of 0.
If the contract is not terminated at the end of 2016, the ceding company will again have the option to terminate the contract at term expiration and receive a profit commission from the reinsurer calculated as follows:
- Profit commission = [35% * Full Term Ceded Premium] – [Full Term Ceded Loss], subject to a minimum of 0.
The reinsurer cannot terminate the contract at any time.

The reinsurer has simulated five trials of the ceding company's loss ratio subject to the aggregate stop loss as follows (values in millions):

Simulation	Accident Year 2016: Loss Ratio	2016: Loss Amount	Accident Year 2017: Loss Ratio	2017: Loss Amount
1	73.9%	517	68.0%	510
2	64.8%	454	67.9%	509
3	66.8%	468	65.5%	491
4	65.6%	459	65.3%	490
5	65.1%	456	58.7%	440
Mean	67.2%	471	65.1%	488

	2016	2017
Subject Premium	700	750
Ceded Premium	9.8	10.5

For each simulation, assume that the ceding company will only terminate the contract if the profit commission payable is greater than zero.

Part a (1 point)

Calculate the expected profit commission payable at the end of 2016.

Calculate the expected profit commission for the full term of the contract.