SOA Exam ASTAM Sample Question 16

Study guide: Exam ASTAM

XYZ Insurer has two lines of insurance business with their aggregate claim payments denoted by S_1 and S_2, respectively.

• S_1 and S_2 are independent and both follow compound Poisson processes.
• S_1 has a Poisson primary distribution with mean \lambda_1 = 2 and severity probabilities 0.3 on a payment of 0 and 0.7 on a payment of 2.
• S_2 has a Poisson primary with mean \lambda_2 = 1 and severity probabilities 0.6 on a payment of 0 and 0.4 on a payment of 4.

Part a

Use the convolution formula to derive the probability function for S_1.

Part b

Show that S = S_1 + S_2 is also a compound Poisson process. Identify the Poisson primary \lambda and the secondary distribution.

Part c

Calculate the probability that the total claim payment amount from XYZ Insurer's all business is 4.

Part d

XYZ Insurer is considering the purchase of stop-loss reinsurance, with an aggregate deductible of 4 on its entire business.

Determine the net stop-loss reinsurance premium.

Answer this question and see the worked solution

Concepts tested

• Compound Poisson Process
• Convolution
• Panjer Recursion
• Stop-Loss Reinsurance
• Aggregate Loss Model
• Probability

More questions from this set

• SOA Exam ASTAM Sample Question 15
• SOA Exam ASTAM Sample Question 17