Exercise 9

The insurer is underwriting 3-month policies covering a specific risk for the premium of 300. A sale of a given quarter is evenly distributed over the quarters period. The same applies to claims: they are evenly distributed over the 3-month period of policys validity.

Year	2012	2013				2014
Quarter	Q4	Q1	Q2	Q3	Q4	Q1
No of written policies	8 000	10 000	12 000	14 000	16 000	18 000

Calculate the premium reserve as of October 31, 2013.

{Hint: Calculate the number of policies, which are in force on October 31. Use as a unit one policy with the duration of 3 months. You should find out, that on October 31, there were

14 0002313 units originated from Q3 and 16 000132,53 . The first fraction stands for the share of active policies in the total number of policies issued in the respective quarter, and the second fraction the average duration of the policy. Finally, you should get R=7 555,56*300=2 266 666.67}