
#1




About a kind of Pareto model
I am reading an old book "Foundations of Casualty Actuarial
Science (Fourth Edition)" by the CAS published in 2001, in order to learn some reinsruance pricing approaches. In Chapter 7 "Reinsurance", there is a model called Censored Pareto model, as shown in the picture attached. However, it can be seen that F(1) is not equal to 1 as there is no definition for x>1. So it is not a reasonable probability model, is it? In addition, when it computed E[x;1], it utilized the limited expected value equation. But the latter only applies to a Pareto distribution which is not censored. So the result seems to have something wrong. Anyone holds interest in that question? Thanks in advance. 
#2




F(1) does equal 1 since you are given that 1F(1) = 0.
There is a point mass at 1 which corresponds to the probability that the uncensored distribution is bigger than 1.
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#3




Okay, so I agree that it is presented funny, but I don't have the full context, so I may be missing something. However, I'm pretty sure the misunderstanding is associated with this line:
Quote:
However, from the perspective of the insurer, reinsurance kicks in once x exceeds 1. There will never be a claim size of 120% of MPL, for example. Since severity is capped at 100%, the "normal" pareto formula for E[X;1] will correctly calculate the expected fraction of MPL for the severity. Riley 
#4




You know, I don't regret missing that game. I told the boys I had to go see about a Pareto model.
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#7




Quote:
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