Lecture Notes 7 - University of Illinois at Urbana

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