Fisher.Understanding
Reading: Fisher, G. et al, "Individual Risk Study Note," CAS Study Note, Version 3, October 2019. Chapter 3. Section 6 and Chapter 4
Synopsis: In this article we finish up the Fisher paper by looking at a couple of leftover topics.
Study Tips
Read this article first and then skim the source text.
Estimated study time: 1 Hour (not including subsequent review time)
BattleTable
Based on past exams, the main things you need to know (in rough order of importance) are:
- fact A...
- fact B...
reference part (a) part (b) part (c) part (d) E (2018.Spring #1) E (2018.Spring #1) E (2018.Spring #1) E (2018.Spring #1) E (2018.Spring #1) E (2018.Spring #1) E (2018.Spring #1) E (2018.Spring #1)
In Plain English!
Understanding Aggregate Loss Distributions
In general, for two risks with the same expected loss, the smaller risk has more variability than a large risk that has a high number of less severe claims.
The distribution of entry ratios (the r values) is mainly shaped by the variance of the severity distribution. However, the distribution of insurance charges (the [math]\phi(r)[/math] values) is driven more by the variance of the claim frequency distribution. To see this it's helpful to consider two extreme cases.
Case 1: Suppose we have a large number of policies, all of which experience exactly one loss of $100. The expected loss is also $100.