Transcript Lecture Notes 9 - University of Illinois at Urbana

Math 479 / 568
Casualty Actuarial Mathematics
Fall 2014
University of Illinois at Urbana-Champaign
Professor Rick Gorvett
Session 9: Risk Classification
September 30, 2014
1
Agenda
• Ratemaking “relativities”
• Risk classification
2
Ratemaking “Relativities”
• Three kinds of relativities
– Classification
– Territorial
– Increased limits
• Classification ratemaking
– One class serves as the “base class” (relativity =
1.00)
– Rates for other classes are keyed off of the base class
rate
• Class rate = base rate × class relativity factor
3
Ratemaking “Relativities” (cont.)
• Classification ratemaking (cont.)
– Ratemaking process
1) Determine indicated overall rate change
2) Determine on-level premium for each class
3) Convert on-level EP by class to a base-class-equivalent by
dividing by the existing class relativities
4) Determine loss ratio for each class, using base-classequivalent on-level EP
5) Determine indicated class relativities by dividing each
class’s loss ratio by the base class loss ratio
6) Use an off-balance factor to determine the base rate
necessary to achieve the overall indicated rate change
7) If necessary, limit rate changes by class to any existing
regulatory restrictions, and adjust to yield the overall
indicated rate change
4
Ratemaking “Relativities” (cont.)
• Territorial ratemaking
– Very similar to classification ratemaking,
conceptually and procedurally
• Increased limits factors
– Basic limits premium or loss cost
• E.g., $100,000 per occurrence limit
– Calculate premiums or loss costs for higher policy
limits by multiplying the basic limits value by the
appropriate increased limits factor (ILF)
5
Risk Classification
• Differential premiums
– Group characteristics determine the class
– Different characteristics imply different underlying
loss propensities, and thus different indicated /
required premiums
• Costs that may vary by group:
– Losses
– Risk – variation from expected values; e.g., more
heterogeneity within a group implies more potential
adverse selection
– Expenses
– Investment income – e.g., long- versus short-tailed
LoBs
6
Risk Classification Rating Variables
• Criteria for selecting rating variables
– Statistical or actuarial
•
•
•
•
Accuracy and fairness
Homogeneity
Credibility
Reliability or predictive stability
– Operational or practical
• Objectively defined
• Administrative expense
• Verifiability
7
Rating Variables (cont.)
• Criteria for selecting rating variables (cont.)
– Social
• Socially acceptable
• Privacy issues
• Causality – intuitively understandable underlying economic
or risk management link of rating variable to insurance cost
• Controllability
• Affordability
– Legal
• State regulations
• Federal equal protection clause
8
2006 CAS Exam 5, #39
9
2004 CAS Exam 5, #36
10