

FlashChat  Actuarial Discussion  Preliminary Exams  CAS/SOA Exams  Cyberchat  Around the World  Suggestions 
DW Simpson 
Actuarial Salary Surveys 
Actuarial Meeting Schedule 
Contact DW Simpson 
ShortTerm Actuarial Math Old Exam C Forum 

Thread Tools  Search this Thread  Display Modes 
#1




STAM  Textbook Example 5.7 Reinsurance Exposure Rating
On example 5.7 in page 183 of the 4th edition of the textbook by Brown and Lennox the authors imply a relationship between Increased Limit Factors ILFs and the cumulative distribution of limited loss. It seems to make sense, but I wanted to know if there was a more solid base for the relationship.
I see that ILFs are similar to ratios of E[X^u] with varying u, one being the basic in the denominator. I can also see that E[X^5,000,000] = 14,000,000, as the exercise mentions it's the highest limit that the insureds can buy, and from there all the others result. The basic would be E[X^500,000) = E[X^5,000,000) / 1.6 = 8,750,000 E[X^1,000,000) = 1.15 * 8,750,000 = 10,062,500 E[X^2,000,000) = 1.35 * 8,750,000 = 11,812,500 and then the losses for the reinsurance layer would be 14,000,000  10,062,500 = 3,937,500. There is a shorter answer. Losses in insurance layer = 70% * 20,000,000 (1  1.15/1.6) = 3,937,500 The reference to the cumulative function is OK, but it was not clear to me directly (even after correcting as per the errata). The cumulative distribution using the losses at different limits would be (using M as millions) F(0.5M) = 8.75/14 = 0.625 F(1M) = 10.0625/14 = 0.71875 F(2M) = 11.8125/14 = 0.84375 F(5M) = 14/14 = 1.000 and are the same as in the book as the ratios of ILFs to the ILF at the high limit of the reinsurance. But there is a shorter way to get to the answer as shown above.
__________________
German ______________ Prelims: VEE: 
Thread Tools  Search this Thread 
Display Modes  

