Reinsurance Pricing

1
Reinsurance Pricing

• Sean Russell
• Occa Meeting
• July 4, 2007

2
Overview

• Basic Reinsurance Pricing Techniques
• Experience Rating
• Exposure Rating
• Modeling
• Application of Actuarial Methods
• Capital Allocation

3
Experience Rating

• Individual Companies loss experience
• Projection forward based on past experience
• Trending
• Layering
• Developing
• Premium

4
Experience Rating
5
Experience Rating Trending/Developing
6
Experience Rating On Level
7
Experience Rating Considerations

• Lack of credible data
• Weighting of individual years
• Changes in Limit profiles
• Changes in mix of business, classes of business
• Legislative changes
• New lines of business
• Excess Leverage effect

8
Exposure Rating

• What to do when there is very little individual
  company data ?
• Exposure rating ?Industry Burning cost
• Exposure curves give distribution of loss
  relative to the insured limit
• With exposure data (limit profile) can then
  develop expected losses
• Loss ratio of portfolio is an important factor
• Source of curves ISO, internal data

9
Loss Modeling

• Mathematical relationships which describe losses
• Typical Reinsurance models
• Pareto distribution for Severity
• Poisson distribution for Frequency
• Log Normal distribution for Loss Ratio
• Mean and Variance are important
• Parameter Uncertainty
• Simulation tools

10
Modeling

• Loss Sensitive Features
• Sliding scale commissions
• Profit commissions
• No Claims Bonus
• Swing Rates
• Deficit Carryforwards
• Payout Patterns/Discounting

11
Capital Allocation

• Why we hold Capital
• Regulators
• Rating Agencies
• Risk
• Risk ? Volatility

12
Historical Results
May include primary business written in same
legal entity. Includes treaty and facultative.
Combined is sum of all legal entities owned by
the same group. Swiss Re premium is gross of
internal quota shares. Allocation of premium,
losses, commisions to casualty (automobile,Liabili
ty) may not be accurate for multiline
treaties. Combined ratio is estimated by adding
average commission/brokerage for each company.
13
Conclusions

• Reinsurance pricing applies similar actuarial
  techniques as primary pricing
• More reliance on statistical methods and
  distributions due to smaller quantity of data
• One step further removed from insured, data
  quality, company knowledge critical