Math 479
Casualty Actuarial Mathematics
Fall 2014
University of Illinois at Urbana-Champaign
Professor Rick Gorvett
Session 7: Ratemaking I
September 16, 2014
1
Agenda
• Ratemaking I
– Overall concept
– Two basic techniques
• Pure premium method
• Loss ratio method
2
Ratemaking:
The Overall Concept
3
Ratemaking Framework
• Ratemaking is an exercise in “what-if”
– “What if an insurer wrote a book of policies
similar to that which it wrote in the past?”
– “What if historical losses (or very similar ones)
were to re-occur in the prospective policy
period? How much would they cost the
insurer?”
– “What if historical policies were re-written at
current rates? What would be the premium?
4
Ratemaking Framework (cont.)
• Is this “what-if” tenable?
• Must address inherent differences between
anticipated future versus past
–
–
–
–
Different types of policyholders / underwriting
Different economic / financial environment
Different judicial / legal atmosphere
Different possible outcomes from stochastic
processes
– Etc, etc.
5
Ratemaking Framework (cont.)
Premium
=
Losses
+
Expenses
+
Load for Profit & Contingencies
6
Ratemaking:
Two Basic Techniques
7
(1) Pure Premium Method
• Project future losses per unit of exposure
• This is the “pure premium” (PP)
• Calculate rate per unit of exposure
Rate =
(PP + FE) ÷ (1 – VE – Profit)
FE = fixed expenses ($)
VE = variable expenses(%)
Profit = profit and contingencies load (%)
8
(2) Loss Ratio Method
• Bring historical premiums to an on-level
(current) basis
• Adjust historical losses for
– Loss development: estimate what the insurer
will ultimately pay out on losses from
historical periods
– Loss trend: adjust losses to reflect changes in
claims costs over time
• Frequency (per unit of exposure) changes
• Severity (per loss) changes
9
(2) Loss Ratio Method (cont.)
• Relate the trended and developed historical
losses to the on-level premium
– Knowing expense and profit loads, this comparison
will indicate whether or not, and to what degree,
current rates need to be changed
• Adjust this indicated rate change, if necessary,
for credibility considerations
• Take the above indicated overall rate change
and spread it to multiple risk classifications and
/ or territories, if necessary
10
(2) Loss Ratio Method (cont.)
• Indicated rate change = {ALR / ELR} – 1
ALR = actual loss ratio = (trended and developed
losses) / (on-level premium)
ELR = expected loss ratio
11
Issues
• Data types and organization
– Losses – paid, incurred,…
– Premiums – written vs earned, gross vs net
– AY vs PY vs CY
• Loss development
• Loss trend
• On-level premium
– Parallelogram method
• Classifications
12
Next Time
• Ratemaking II
– Trend vs development – is there overlap?
– Basic vs total limits losses
– Parallelogram method
13