Fisher.CaseStudy
Reading: Fisher, G. et al, "Individual Risk Study Note," CAS Study Note, Version 3, October 2019. Case Study.
Synopsis: The case study is meant to help you learn some of the concepts from the Fisher paper.
Study Tips
The case study doesn't have great instructions so we've added commentary and helpful formulas for each step in this wiki companion article.
Estimated study time: 2 Hours (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!
Alice: "If you haven't already, download the latest version of the case study from the CAS website here: Fisher Case Study. Now let's open up the case study and get started".
Step 1
- Create a new column called "Natural Log". The values in this column are the natural log of the loss amount (=LN(loss)).
- Estimate μ as the average of the Natural Log column. Similarly, estimate σ as the population standard deviation of the Natural Log column (Excel =StDev.P(column))
- Fill in the summary matrix below
| Fitted | Empirical | |
| Mean | ||
| Standard Deviation |
- Empirical values are found by taking the average and population standard deviation of the loss column respectively.
- Fitted values use the parameter estimates in the following formulas from Bahnemann Chapter 2.4 for a lognormal distribution, X.
- [math]E[X]=e^{\mu+\frac{\sigma^2}{2}}[/math]
- [math]Var(X)=\left(e^{\sigma^2}-1\right)\cdot e^{2\mu+\sigma^2}[/math]
Alice: "Me again, you did remember to skim through Bahnemann Chapters 1 - 4 even though they're only recommended reading on the syllabus didn't you..."